The robust stability of uncertain linear degenerate systems with discrete and distributed delays is studied in this paper. The uncertainties under consideration are norm bounded, and possibly time varying. A novel rob...The robust stability of uncertain linear degenerate systems with discrete and distributed delays is studied in this paper. The uncertainties under consideration are norm bounded, and possibly time varying. A novel robust stability criterion of the system is derived by constructing Lyapunov functions. The degenerate systems are transformed to a descriptor system and the stability criteria are formulated in the form of a linear matrix inequality （LMI）. Therefore, it is easy to check the robust stability of the degenerate systems by using this method. Numerical examples are also worked out to illustrate the obtained results.展开更多
The decentralized stabilization of continuous and discrete linear large scale systems with symmetric circulant structure was studied.A few sufficient conditions on decentralized stabilization of such systems were prop...The decentralized stabilization of continuous and discrete linear large scale systems with symmetric circulant structure was studied.A few sufficient conditions on decentralized stabilization of such systems were proposed.For the continuous systems,by introducing a concept called the magnitude of interconnected structure,a very important property that the decentralized stabilization of such systems is fully determined by the structure of each isolated subsystem that is obtained when the magnitude of interconnected structure of the overall system is given.So the decentralized stabilization of such systems can be got by only appropriately designing or modifying the structure of each isolated subsystem,no matter how complicated the interconnected structure of the overall system is.A algorithm for obtaining decentralized state feedback to stabilize the overall system is given.The discrete systems were also discussed.The results show that there is a great dfference on decentralized stabilization between continuous case and discrete case.展开更多
In this paper,an HIV dynamics model with the proliferation of CD4 T cells is proposed.The authors consider nonnegativity,boundedness,global asymptotic stability of the solutions and bifurcation properties of the stead...In this paper,an HIV dynamics model with the proliferation of CD4 T cells is proposed.The authors consider nonnegativity,boundedness,global asymptotic stability of the solutions and bifurcation properties of the steady states.It is proved that the virus is cleared from the host under some conditions if the basic reproduction number R0 is less than unity.Meanwhile,the model exhibits the phenomenon of backward bifurcation.We also obtain one equilibrium is semi-stable by using center manifold theory.It is proved that the endemic equilibrium is globally asymptotically stable under some conditions if R0 is greater than unity.It also is proved that the model undergoes Hopf bifurcation from the endemic equilibrium under some conditions.It is novelty that the model exhibits two famous bifurcations,backward bifurcation and Hopf bifurcation.The model is extended to incorporate the specific Cytotoxic T Lymphocytes(CTLs)immune response.Stabilities of equilibria and Hopf bifurcation are considered accordingly.In addition,some numerical simulations for justifying the theoretical analysis results are also given in paper.展开更多
The main purpose of this paper is to examine the existence of coupled solutions and coupled minimal-maximal solutions for a kind of nonlinear operator equations in partial ordered linear topology spaces by employing t...The main purpose of this paper is to examine the existence of coupled solutions and coupled minimal-maximal solutions for a kind of nonlinear operator equations in partial ordered linear topology spaces by employing the semi-order method. Some new existence results are obtained.展开更多
In this paper, a class of mixed monotone operators is studied. Some new fixed point theorems are presented by means of partial order theory, and the uniqueness and existence of fixed points are obtained without assumi...In this paper, a class of mixed monotone operators is studied. Some new fixed point theorems are presented by means of partial order theory, and the uniqueness and existence of fixed points are obtained without assuming the operator to be compact or continuous. Our conclusions extend the relevant results. Moreover,as an application of our result, the existence and uniqueness of positive solution for a class of fractional differential equation boundary value problem are proved.展开更多
In the paper, we take up a new method to prove a result of value distribution of meromorphic functions: let f be a meromorphic function in , and let , where P is a polynomial. Suppose that all zeros of f have multipli...In the paper, we take up a new method to prove a result of value distribution of meromorphic functions: let f be a meromorphic function in , and let , where P is a polynomial. Suppose that all zeros of f have multiplicity at least , except possibly finite many, and as . Then has infinitely many zeros.展开更多
In the paper,we get the precise results of Hájek-Rényi type inequalities for the partial sums of negatively orthant dependent sequences,which improve the results of Theorem 3.1and Corollary 3.2 in Kim(2006)a...In the paper,we get the precise results of Hájek-Rényi type inequalities for the partial sums of negatively orthant dependent sequences,which improve the results of Theorem 3.1and Corollary 3.2 in Kim(2006)and the strong law of large numbers and strong growth rate for negatively orthant dependent sequences.展开更多
In this paper,we study a new class of differential quasivariational-hemivariational inequalities of the elliptic type.The problem consists of a system coupling the Cauchy problem for an ordinary differential equation ...In this paper,we study a new class of differential quasivariational-hemivariational inequalities of the elliptic type.The problem consists of a system coupling the Cauchy problem for an ordinary differential equation with the variational-hemivariational inequalities,unilateral constraints,and history-dependent operators.First,based on the Minty formulation and the continuity of the solution map of a parametrized quasivariational-hemivariational inequality,and a fixed point theorem for a history-dependent operator,we prove a result on the well-posedness.Next,we examine optimal control problems for differential quasivariational-hemivariational inequalities,including a time-optimal control problem and a maximum stay control problem,for which we show the existence of solutions.In all the optimal control problems,the system is controlled through a distributed and boundary control,a control in initial conditions,and a control that appears in history-dependent operators.Finally,we illustrate the results by considering a nonlinear controlled system for a time-dependent elliptic equation with unilateral constraints.展开更多
This article is focusing on a class of multi-delay predator-prey model with feedback controls and prey diffusion. By developing some new analysis methods and using the theory of differential inequalities as well as co...This article is focusing on a class of multi-delay predator-prey model with feedback controls and prey diffusion. By developing some new analysis methods and using the theory of differential inequalities as well as constructing a suitable Lyapunov function, we establish a set of easily verifiable sufficient conditions which guarantee the permanence of the system and the globally attractivity of positive solution for the predator-prey system.Furthermore, some conditions for the existence, uniqueness and stability of positive periodic solution for the corresponding periodic system are obtained by using the fixed point theory and some new analysis techniques. In additional, some numerical solutions of the equations describing the system are given to verify the obtained criteria are new, general, and easily verifiable. Finally, we still solve numerically the corresponding stochastic predator-prey models with multiplicative noise sources, and obtain some new interesting dynamical behaviors of the system.展开更多
The robust stability of uncertain neutral systems with mixed time-varying delays is investigated in this paper. The uncertainties under consideration are norm-bounded and time-varying. Based on the Lyapunov stability ...The robust stability of uncertain neutral systems with mixed time-varying delays is investigated in this paper. The uncertainties under consideration are norm-bounded and time-varying. Based on the Lyapunov stability theory, a delay-dependent stability criterion is derived and given in the form of a linear matrix inequality （LMI）. Finally, a numerical example is given to illustrate significant improvement over some existing results.展开更多
An H∞ filter design for linear time delay system with randomly varying sensor delay is investigated.The delay considered here is assumed to satisfy a certain stochastic characteristic.A stochastic variable satisfying...An H∞ filter design for linear time delay system with randomly varying sensor delay is investigated.The delay considered here is assumed to satisfy a certain stochastic characteristic.A stochastic variable satisfying Bernoulli random binary distribution is introduced and a new system model is established by employing the measurements with random delay.By using the linear matrix inequality(LMI) technique,sufficient conditions are derived for ensuring the mean-square stochastic stability of the filtering error systems and guaranteeing a prescribed H∞ filtering performance.Finally,a numerical example is given to demonstrate the effectiveness of the proposed approach.展开更多
In this paper,the preimage branch t-entropy and entropy dimension for nonautonomous systems are studied and some systems with preimage branch t-entropy zero are introduced.Moreover,formulas calculating the s-topologic...In this paper,the preimage branch t-entropy and entropy dimension for nonautonomous systems are studied and some systems with preimage branch t-entropy zero are introduced.Moreover,formulas calculating the s-topological entropy of a sequence of equi-continuous monotone maps on the unit circle are given.Finally,examples to show that the entropy dimension of non-autonomous systems can be attained by any positive number s are constructed.展开更多
The goal of this paper is to study a mathematical model of a nonlinear static frictional contact problem in elasticity with the mixed boundary conditions described by a combination of the Signorini unilateral friction...The goal of this paper is to study a mathematical model of a nonlinear static frictional contact problem in elasticity with the mixed boundary conditions described by a combination of the Signorini unilateral frictionless contact condition,and nonmonotone multivalued contact,and friction laws of subdifferential form.First,under suitable assumptions,we deliver the weak formulation of the contact model,which is an elliptic system with Lagrange multipliers,and which consists of a hemivariational inequality and a variational inequality.Then,we prove the solvability of the contact problem.Finally,employing the notion of H-convergence of nonlinear elasticity tensors,we provide a result on the convergence of solutions under perturbations which appear in the elasticity operator,body forces,and surface tractions.展开更多
In 2010,Gábor Czédli and E.Tamás Schmidt mentioned that the best cover-preserving embedding of a given semimodular lattice is not known yet[A cover-preserving embedding of semimodular lattices into geom...In 2010,Gábor Czédli and E.Tamás Schmidt mentioned that the best cover-preserving embedding of a given semimodular lattice is not known yet[A cover-preserving embedding of semimodular lattices into geometric lattices.Advances in Mathematics,225,2455-2463(2010)].That is to say:What are the geometric lattices G such that a given finite semimodular lattice L has a cover-preserving embedding into G with the smallest|G|?In this paper,we propose an algorithm to calculate all the best extending cover-preserving geometric lattices G of a given semimodular lattice L and prove that the length and the number of atoms of every best extending cover-preserving geometric lattice G equal the length of L and the number of non-zero join-irreducible elements of L,respectively.Therefore,we solve the problem on the best cover-preserving embedding of a given semimodular lattice raised by Gábor Czédli and E.Tamás Schmidt.展开更多
Let G be a finite group, and let A be a proper subgroup of G. Then any chief factor H/AG of G is called a G-boundary factor of A. For any G- boundary factor H/AG of A, the subgroup （A ∩ H）/AG of G/AG is called a G-...Let G be a finite group, and let A be a proper subgroup of G. Then any chief factor H/AG of G is called a G-boundary factor of A. For any G- boundary factor H/AG of A, the subgroup （A ∩ H）/AG of G/AG is called a G-trace of A. In this paper, we prove that G is p-soluble if and only if every maximal chain of G of length 2 contains a proper subgroup M of G such that either some G-trace of M is subnormal or every G-boundary factor of M is a p′- group. This result give a positive answer to a recent open problem of Guo and Skiba. We also give some new characterizations of p-hypercyclically embedded subgroups.展开更多
A physiological model with delay is considered. The time delay being regarded as a parameter, a group of conditions that guarantee the model have multiple periodic solutions is obtained by the global Hopf bifurcation ...A physiological model with delay is considered. The time delay being regarded as a parameter, a group of conditions that guarantee the model have multiple periodic solutions is obtained by the global Hopf bifurcation theorem for FDE and Bendixson＇s criterion for high-dimensional ODE. The results are illustrated by some numerical simulations.展开更多
A system of delay differential equations is studied which represent a model for four neurons with time delayed connections between the neurons and time delayed feedback from each neuron to itself. The linear stability...A system of delay differential equations is studied which represent a model for four neurons with time delayed connections between the neurons and time delayed feedback from each neuron to itself. The linear stability and bifurcation of the system are studied in a parameter space consisting of the sum of the time delays between the elements and the product of the strengths of the connections between the elements. Meanwhile, the bifurcation set are drawn in the parameter space.展开更多
Based on the Kirchhoff transformation and the natural boundary element method, we investigate a coupled natural boundary element method and finite element method for quasi-linear problems in a bounded or unbounded dom...Based on the Kirchhoff transformation and the natural boundary element method, we investigate a coupled natural boundary element method and finite element method for quasi-linear problems in a bounded or unbounded domain with a concave angle. By the principle of the natural boundary reduction, we obtain natural integral equation on circular arc artificial boundaries, and get the coupled variational problem and its numerical method. Moreover, the convergence of approximate solutions and error estimates are obtained. Finally, some numerical examples are presented to show the feasibility of our method. Our work can be viewed as an extension of the existing work of H.D. Han et al..展开更多
In this paper the asymptotieal stability in p-moment of neutral stochastic differential equations with discrete and distributed time-varying delays is discussed. The authors apply the fixed-point theory rather than th...In this paper the asymptotieal stability in p-moment of neutral stochastic differential equations with discrete and distributed time-varying delays is discussed. The authors apply the fixed-point theory rather than the Lyapunov functions. We give a sufficient condition for asymptotical stability in p-moment when the coefficient functions of equations are not required to be fixed values. Since more general form of system is considered, this paper improves Luo Jiaowan＇s results.展开更多
Let f ： M → M be a partially hyperbolic diffeomorphism on a closed Riemannian manifold with uniformly compact center foliation. We show that if the center foliation of f is of dimension one then the topological entr...Let f ： M → M be a partially hyperbolic diffeomorphism on a closed Riemannian manifold with uniformly compact center foliation. We show that if the center foliation of f is of dimension one then the topological entropy is constant on a small C1 neighborhood of f.展开更多
文摘The robust stability of uncertain linear degenerate systems with discrete and distributed delays is studied in this paper. The uncertainties under consideration are norm bounded, and possibly time varying. A novel robust stability criterion of the system is derived by constructing Lyapunov functions. The degenerate systems are transformed to a descriptor system and the stability criteria are formulated in the form of a linear matrix inequality （LMI）. Therefore, it is easy to check the robust stability of the degenerate systems by using this method. Numerical examples are also worked out to illustrate the obtained results.
文摘The decentralized stabilization of continuous and discrete linear large scale systems with symmetric circulant structure was studied.A few sufficient conditions on decentralized stabilization of such systems were proposed.For the continuous systems,by introducing a concept called the magnitude of interconnected structure,a very important property that the decentralized stabilization of such systems is fully determined by the structure of each isolated subsystem that is obtained when the magnitude of interconnected structure of the overall system is given.So the decentralized stabilization of such systems can be got by only appropriately designing or modifying the structure of each isolated subsystem,no matter how complicated the interconnected structure of the overall system is.A algorithm for obtaining decentralized state feedback to stabilize the overall system is given.The discrete systems were also discussed.The results show that there is a great dfference on decentralized stabilization between continuous case and discrete case.
基金The Teacher Research Capacity Promotion Program of Beijing Normal University Zhuhaithe NSF(11871108)of China
文摘In this paper,an HIV dynamics model with the proliferation of CD4 T cells is proposed.The authors consider nonnegativity,boundedness,global asymptotic stability of the solutions and bifurcation properties of the steady states.It is proved that the virus is cleared from the host under some conditions if the basic reproduction number R0 is less than unity.Meanwhile,the model exhibits the phenomenon of backward bifurcation.We also obtain one equilibrium is semi-stable by using center manifold theory.It is proved that the endemic equilibrium is globally asymptotically stable under some conditions if R0 is greater than unity.It also is proved that the model undergoes Hopf bifurcation from the endemic equilibrium under some conditions.It is novelty that the model exhibits two famous bifurcations,backward bifurcation and Hopf bifurcation.The model is extended to incorporate the specific Cytotoxic T Lymphocytes(CTLs)immune response.Stabilities of equilibria and Hopf bifurcation are considered accordingly.In addition,some numerical simulations for justifying the theoretical analysis results are also given in paper.
基金The Innovation Foundation for College Research Team of Shanxi University of Finance and Economics
文摘The main purpose of this paper is to examine the existence of coupled solutions and coupled minimal-maximal solutions for a kind of nonlinear operator equations in partial ordered linear topology spaces by employing the semi-order method. Some new existence results are obtained.
基金The NSF(201701D0503-9)of Shanxi Provincethe Innovation Foundation for College Teaching Team of Shanxi University of Finance and Economics2015 Education and Teaching Reform Project(2015234)of Shanxi University of Finance and Economics
文摘In this paper, a class of mixed monotone operators is studied. Some new fixed point theorems are presented by means of partial order theory, and the uniqueness and existence of fixed points are obtained without assuming the operator to be compact or continuous. Our conclusions extend the relevant results. Moreover,as an application of our result, the existence and uniqueness of positive solution for a class of fractional differential equation boundary value problem are proved.
文摘In the paper, we take up a new method to prove a result of value distribution of meromorphic functions: let f be a meromorphic function in , and let , where P is a polynomial. Suppose that all zeros of f have multiplicity at least , except possibly finite many, and as . Then has infinitely many zeros.
基金Foundation of Anhui Educational Committee(No.KJ2013Z225)
文摘In the paper,we get the precise results of Hájek-Rényi type inequalities for the partial sums of negatively orthant dependent sequences,which improve the results of Theorem 3.1and Corollary 3.2 in Kim(2006)and the strong law of large numbers and strong growth rate for negatively orthant dependent sequences.
基金supported by National Natural Science Foundation of China(Grant No.12171070)the Central Guidance on Local Science and Technology Development Fund of Sichuan Province(Grant No.2021ZYD0002)+3 种基金supported by the China Scholarship Council(Grant No.202106070120)supported by the European Union’s Horizon 2020 Research and Innovation Program under the Marie Sk?odowska-Curie Grant(Grant No.823731 CONMECH)the Ministry of Science and Higher Education of Poland(Grant Nos.4004/GGPJII/H2020/2018/0 and 440328/PnH2/2019)the National Science Center of Poland(Grant No.2021/41/B/ST1/01636)。
文摘In this paper,we study a new class of differential quasivariational-hemivariational inequalities of the elliptic type.The problem consists of a system coupling the Cauchy problem for an ordinary differential equation with the variational-hemivariational inequalities,unilateral constraints,and history-dependent operators.First,based on the Minty formulation and the continuity of the solution map of a parametrized quasivariational-hemivariational inequality,and a fixed point theorem for a history-dependent operator,we prove a result on the well-posedness.Next,we examine optimal control problems for differential quasivariational-hemivariational inequalities,including a time-optimal control problem and a maximum stay control problem,for which we show the existence of solutions.In all the optimal control problems,the system is controlled through a distributed and boundary control,a control in initial conditions,and a control that appears in history-dependent operators.Finally,we illustrate the results by considering a nonlinear controlled system for a time-dependent elliptic equation with unilateral constraints.
基金supported by the Sichuan Science and Technology Program of China(2018JY0480)the Natural Science Foundation Project of CQ CSTC of China(cstc2015jcyjBX0135)the National Nature Science Fundation of China(61503053)
文摘This article is focusing on a class of multi-delay predator-prey model with feedback controls and prey diffusion. By developing some new analysis methods and using the theory of differential inequalities as well as constructing a suitable Lyapunov function, we establish a set of easily verifiable sufficient conditions which guarantee the permanence of the system and the globally attractivity of positive solution for the predator-prey system.Furthermore, some conditions for the existence, uniqueness and stability of positive periodic solution for the corresponding periodic system are obtained by using the fixed point theory and some new analysis techniques. In additional, some numerical solutions of the equations describing the system are given to verify the obtained criteria are new, general, and easily verifiable. Finally, we still solve numerically the corresponding stochastic predator-prey models with multiplicative noise sources, and obtain some new interesting dynamical behaviors of the system.
文摘The robust stability of uncertain neutral systems with mixed time-varying delays is investigated in this paper. The uncertainties under consideration are norm-bounded and time-varying. Based on the Lyapunov stability theory, a delay-dependent stability criterion is derived and given in the form of a linear matrix inequality （LMI）. Finally, a numerical example is given to illustrate significant improvement over some existing results.
基金National Natural Science Foundations of China (No. 60474079,No. 60704024,No. 60774060,No. 61074025,and No. 61074024)
文摘An H∞ filter design for linear time delay system with randomly varying sensor delay is investigated.The delay considered here is assumed to satisfy a certain stochastic characteristic.A stochastic variable satisfying Bernoulli random binary distribution is introduced and a new system model is established by employing the measurements with random delay.By using the linear matrix inequality(LMI) technique,sufficient conditions are derived for ensuring the mean-square stochastic stability of the filtering error systems and guaranteeing a prescribed H∞ filtering performance.Finally,a numerical example is given to demonstrate the effectiveness of the proposed approach.
基金Lin Wang is supported by the National Natural Science Foundation of China(No.11801336,11771118)the Science and Technology Innovation Project of Shanxi Higher Education(No.2019L0475)the Applied Basic Research Program of Shanxi Province(No:201901D211417).
文摘In this paper,the preimage branch t-entropy and entropy dimension for nonautonomous systems are studied and some systems with preimage branch t-entropy zero are introduced.Moreover,formulas calculating the s-topological entropy of a sequence of equi-continuous monotone maps on the unit circle are given.Finally,examples to show that the entropy dimension of non-autonomous systems can be attained by any positive number s are constructed.
基金The project supported by the NNSF of China Grants Nos.12001478,12026255,12026256 and 11961074,H2020-MSCA-RISE-2018 ResearchInnovation Staff Exchange Scheme Fellowship within the Project No.823731 CONMECH+3 种基金National Science Center of Poland under Preludium Project No.2017/25/N/ST1/00611It is also supported by the Startup Project of Doctor Scientific Research of Yulin Normal University No.G2020ZK07Natural Science Foundation of Guangxi Province Grants Nos.2018GXNSFDA281028 and 2020GXNSFBA297137the High Level Innovation Team Program from Guangxi Higher Education Institutions of China(Document no.[2018]35).
文摘The goal of this paper is to study a mathematical model of a nonlinear static frictional contact problem in elasticity with the mixed boundary conditions described by a combination of the Signorini unilateral frictionless contact condition,and nonmonotone multivalued contact,and friction laws of subdifferential form.First,under suitable assumptions,we deliver the weak formulation of the contact model,which is an elliptic system with Lagrange multipliers,and which consists of a hemivariational inequality and a variational inequality.Then,we prove the solvability of the contact problem.Finally,employing the notion of H-convergence of nonlinear elasticity tensors,we provide a result on the convergence of solutions under perturbations which appear in the elasticity operator,body forces,and surface tractions.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11901064 and 12071325)。
文摘In 2010,Gábor Czédli and E.Tamás Schmidt mentioned that the best cover-preserving embedding of a given semimodular lattice is not known yet[A cover-preserving embedding of semimodular lattices into geometric lattices.Advances in Mathematics,225,2455-2463(2010)].That is to say:What are the geometric lattices G such that a given finite semimodular lattice L has a cover-preserving embedding into G with the smallest|G|?In this paper,we propose an algorithm to calculate all the best extending cover-preserving geometric lattices G of a given semimodular lattice L and prove that the length and the number of atoms of every best extending cover-preserving geometric lattice G equal the length of L and the number of non-zero join-irreducible elements of L,respectively.Therefore,we solve the problem on the best cover-preserving embedding of a given semimodular lattice raised by Gábor Czédli and E.Tamás Schmidt.
基金Acknowledgements The authors were grateful to the referees for their careful reading and helpful suggestions. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11371335, 11471055） and Wu Wen-Tsun Key Laboratory of Mathematics of Chinese Academy of Sciences.
文摘Let G be a finite group, and let A be a proper subgroup of G. Then any chief factor H/AG of G is called a G-boundary factor of A. For any G- boundary factor H/AG of A, the subgroup （A ∩ H）/AG of G/AG is called a G-trace of A. In this paper, we prove that G is p-soluble if and only if every maximal chain of G of length 2 contains a proper subgroup M of G such that either some G-trace of M is subnormal or every G-boundary factor of M is a p′- group. This result give a positive answer to a recent open problem of Guo and Skiba. We also give some new characterizations of p-hypercyclically embedded subgroups.
基金Supported by the National Natural Science Foundation of China ‘Existence and stability of solutions for repulsive periodic systems with weak singularity’(No.11426113)
文摘A physiological model with delay is considered. The time delay being regarded as a parameter, a group of conditions that guarantee the model have multiple periodic solutions is obtained by the global Hopf bifurcation theorem for FDE and Bendixson＇s criterion for high-dimensional ODE. The results are illustrated by some numerical simulations.
文摘A system of delay differential equations is studied which represent a model for four neurons with time delayed connections between the neurons and time delayed feedback from each neuron to itself. The linear stability and bifurcation of the system are studied in a parameter space consisting of the sum of the time delays between the elements and the product of the strengths of the connections between the elements. Meanwhile, the bifurcation set are drawn in the parameter space.
基金Acknowledgments. We would like to thank the reviewers for their valuable comments which improve the paper. This research is partly supported by the National Natural Science Foundation of China contact/grant number： 11071109 Foundation for Innovative Program of Jiangsu Province, contact/grant number： CXZZ12_0383 and CXZZ11_0870.
文摘Based on the Kirchhoff transformation and the natural boundary element method, we investigate a coupled natural boundary element method and finite element method for quasi-linear problems in a bounded or unbounded domain with a concave angle. By the principle of the natural boundary reduction, we obtain natural integral equation on circular arc artificial boundaries, and get the coupled variational problem and its numerical method. Moreover, the convergence of approximate solutions and error estimates are obtained. Finally, some numerical examples are presented to show the feasibility of our method. Our work can be viewed as an extension of the existing work of H.D. Han et al..
基金Supported by the National Natural Science Foundation of China (Grant Nos.6073602930570507)the National Basic Research Program of China (Grant No.2010CB732501)
文摘In this paper the asymptotieal stability in p-moment of neutral stochastic differential equations with discrete and distributed time-varying delays is discussed. The authors apply the fixed-point theory rather than the Lyapunov functions. We give a sufficient condition for asymptotical stability in p-moment when the coefficient functions of equations are not required to be fixed values. Since more general form of system is considered, this paper improves Luo Jiaowan＇s results.
基金supported by NSFC(No:11371120)GCCHB(No:GCC2014052)supported by NSFHB(No:A2014205154)
文摘Let f ： M → M be a partially hyperbolic diffeomorphism on a closed Riemannian manifold with uniformly compact center foliation. We show that if the center foliation of f is of dimension one then the topological entropy is constant on a small C1 neighborhood of f.
