Let f be a twice continuously differentiable self-mapping of a unit disk satisfying Poisson differential inequality |△f(z)| ≤ B · |Df(z)|^(2) for some B > 0 and f(0) = 0. In this note, we show that f does no...Let f be a twice continuously differentiable self-mapping of a unit disk satisfying Poisson differential inequality |△f(z)| ≤ B · |Df(z)|^(2) for some B > 0 and f(0) = 0. In this note, we show that f does not always satisfy the Schwarz-Pick type inequality (1-|z|^(2))/(1-|f(z)|^(2))≤ C(B),where C(B) is a constant depending only on B. Moreover, a more general Schwarz-Pick type inequality for mapping that satisfies general Poisson differential inequality is established under certain conditions.展开更多
In this paper, we obtain a slight generalization of the celebrated Halanay delay differential inequality[1]. Using this inequality, Liapunov function and vector Liapunov function, we show that our result can be applie...In this paper, we obtain a slight generalization of the celebrated Halanay delay differential inequality[1]. Using this inequality, Liapunov function and vector Liapunov function, we show that our result can be applied to the stability behavior of solutions of some delay differential systems. And also, we attempt to relax some restrictions of dv/dt, which is necessary under Liapunov function's method on the delay differential systems.展开更多
In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery p...In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery problem for such differential operator is considered.展开更多
In this paper,making use of upper and lower solutions,we first prove the existence of the solu tion for integral differential equation of Volterra type.Then applying the theory of differential in equalities obtained,u...In this paper,making use of upper and lower solutions,we first prove the existence of the solu tion for integral differential equation of Volterra type.Then applying the theory of differential in equalities obtained,under the appropriate assumptions,by constructing the special function of upper and lower solutions,we demonstrate the existence of the solution for singularly preturbed integral differential equation of Volterra type,and give the uniformly valid approximate estimation.展开更多
By using some differential inequality, a second-order delay differential equation(r(t)x′(t))′ + p(t)x(q(t)) = 0has been investigated and some necessary condition for this equation has a nonoscillatorysolution and so...By using some differential inequality, a second-order delay differential equation(r(t)x′(t))′ + p(t)x(q(t)) = 0has been investigated and some necessary condition for this equation has a nonoscillatorysolution and some sufficient condition which ensures that all of the solutions of the aboveequation are oscillatory are obtained.展开更多
In this paper, using the theory of differential inequalities, we study the nonlinear boundary value problem for a class of integro-differential system. Under appropriate assumptions, the existence of solution is prove...In this paper, using the theory of differential inequalities, we study the nonlinear boundary value problem for a class of integro-differential system. Under appropriate assumptions, the existence of solution is proved and the uniformly valid asymptotic expansions for arbitrary n-th order approximation and the estimation of remainder term are obtained simply and conveniently.展开更多
In this paper, the boundary value problem of quasilinear differential equation with two parameters is studied via differential inequalities. The asymptotic solution is found and the remainders is estimated.
In this paper,we study the singular perturbation of boundary value problem of systems for quasilinear ordinary differential equations:x'=j(i,x,y,ε),εy'=g(t,x,y,ε)y'+h(t,x,y,ε),y(0,ε)=A(ε),y(0,ε)=B(...In this paper,we study the singular perturbation of boundary value problem of systems for quasilinear ordinary differential equations:x'=j(i,x,y,ε),εy'=g(t,x,y,ε)y'+h(t,x,y,ε),y(0,ε)=A(ε),y(0,ε)=B(ε),y(1,ε)=C(ε)where xf.y,h,A,B and C belong to Rn and a is a diagonal matrix.Under the appropriate assumptions,using the technique of diagonalization and the theory of differential inequalities we obtain the existence of solution and its componentwise uniformly valid asymptotic estimation.展开更多
In this paper, positiveness theorems of solutions for several differential inequalities are proved and are used to prove the existence of traveling wave front solutions of reaction-diffusion systems. As an application...In this paper, positiveness theorems of solutions for several differential inequalities are proved and are used to prove the existence of traveling wave front solutions of reaction-diffusion systems. As an application, two examples are given.展开更多
In this paper,a kind of boundary value problems for Volterra functional differential equation is studied.\$\$εx″(t)=f(t,x(t),\(t),x(t-τ),x′(t),ε),t∈(0,1), x(t)=φ(t,ε),t∈[-τ,0], ax(1)+bx′(1)=A(ε).\$\$\ \ B...In this paper,a kind of boundary value problems for Volterra functional differential equation is studied.\$\$εx″(t)=f(t,x(t),\(t),x(t-τ),x′(t),ε),t∈(0,1), x(t)=φ(t,ε),t∈[-τ,0], ax(1)+bx′(1)=A(ε).\$\$\ \ By using the theory of differential inequality,the author proves the existence of the solutions and a uniformly valid asymptotic expansion of the solution is given as well.展开更多
In this paper,we consider a new differential variational inequality（DVI,for short）which is composed of an evolution equation and a variational inequality in infinite Banach spaces.This kind of problems may be regard...In this paper,we consider a new differential variational inequality（DVI,for short）which is composed of an evolution equation and a variational inequality in infinite Banach spaces.This kind of problems may be regarded as a special feedback control problem.Based on the Browder＇s theorem and the optimal control theory,we show the existence of solutions to the mentioned problem.展开更多
In this article, a new differential inverse variational inequality is introduced and studied in finite dimensional Euclidean spaces. Some results concerned with the linear growth of the solution set for the differenti...In this article, a new differential inverse variational inequality is introduced and studied in finite dimensional Euclidean spaces. Some results concerned with the linear growth of the solution set for the differential inverse variational inequalities are obtained under different conditions. Some existence theorems of Caratheodory weak solutions for the differential inverse variational inequality are also established under suitable conditions. An application to the time-dependent spatial price equilibrium control problem is also given.展开更多
This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space.Utilizing the KKM theorem,a result concerned with the upper semicontinuity and measur...This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space.Utilizing the KKM theorem,a result concerned with the upper semicontinuity and measurability of the solution set of a hemivariational inequality is established.By using a fixed point theorem for a condensing setvalued map,the nonemptiness and compactness of the set of mild solutions are also obtained for such a system under mild conditions.Finally,an example is presented to illustrate our main results.展开更多
In this paper we proved the A(p)-weighted inequalities for martingale transforms and differential subordinations of Banach-space-valued regular maringales. We discussed the relations between the weighted inequalities,...In this paper we proved the A(p)-weighted inequalities for martingale transforms and differential subordinations of Banach-space-valued regular maringales. We discussed the relations between the weighted inequalities, A(p)-weight functions and the Banach spaces which has the UMD property or are isomorphic to Hilbert space.展开更多
We consider a differential variational-hemivariational inequality with constraints,in the framework of reflexive Banach spaces.The existence of a unique mild solution of the inequality,together with its stability,was ...We consider a differential variational-hemivariational inequality with constraints,in the framework of reflexive Banach spaces.The existence of a unique mild solution of the inequality,together with its stability,was proved in[1].Here,we complete these results with existence,uniqueness and convergence results for an associated penalty-type method.To this end,we construct a sequence of perturbed differential variational-hemivariational inequalities governed by perturbed sets of constraints and penalty coefficients.We prove the unique solvability of each perturbed inequality as well as the convergence of its solution to the solution of the original inequality.Then,we consider a mathematical model which describes the equilibrium of a viscoelastic rod in unilateral contact.The weak formulation of the model is in a form of a differential variational-hemivariational inequality in which the unknowns are the displacement field and the history of the deformation.We apply our abstract penalty method in the study of this inequality and provide the corresponding mechanical interpretations.展开更多
This paper investigates the nonemptiness and compactness of the mild solution set for a class of Riemann-Liouville fractional delay differential variational inequalities,which are formulated by a Riemann-Liouville fra...This paper investigates the nonemptiness and compactness of the mild solution set for a class of Riemann-Liouville fractional delay differential variational inequalities,which are formulated by a Riemann-Liouville fractional delay evolution equation and a variational inequality.Our approach is based on the resolvent technique and a generalization of strongly continuous semigroups combined with Schauder's fixed point theorem.展开更多
The goal of this paper is to deal with a new dynamic system called a differential evolution hemivariational inequality(DEHVI)which couples an abstract parabolic evolution hemivariational inequality and a nonlinear dif...The goal of this paper is to deal with a new dynamic system called a differential evolution hemivariational inequality(DEHVI)which couples an abstract parabolic evolution hemivariational inequality and a nonlinear differential equation in a Banach space.First,by apply ing surjectivity result for pseudomonotone multivalued mappins and the properties of Clarke's subgradient,we show the nonempty of the solution set for the parabolic hemivariational inequality.Then,some topological properties of the solution set are established such as boundedness,closedness and convexity.Furthermore,we explore the upper semicontinuity of the solution mapping.Finally,we prove the solution set of the system(DEHVI)is nonempty and the set of all trajectories of(DEHVI)is weakly compact in C(I,X).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
In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solu...In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solution is proved and the uniformly valid asymptotic expansions is obtained as well.展开更多
基金supported by NNSF of China(11701111)NNSFs of Guangdong Province (2016A030310257 and 2015A030313346)the Visiting Scholar Program of Chern Institute of Mathematics at Nankai University when the authors worked as visiting scholars。
文摘Let f be a twice continuously differentiable self-mapping of a unit disk satisfying Poisson differential inequality |△f(z)| ≤ B · |Df(z)|^(2) for some B > 0 and f(0) = 0. In this note, we show that f does not always satisfy the Schwarz-Pick type inequality (1-|z|^(2))/(1-|f(z)|^(2))≤ C(B),where C(B) is a constant depending only on B. Moreover, a more general Schwarz-Pick type inequality for mapping that satisfies general Poisson differential inequality is established under certain conditions.
基金Supported by the National Natural Science Foundation of China (60274007) Significant Academic Foundation of Education Department of Hubei Province (2001Z06003).
文摘In this paper, we obtain a slight generalization of the celebrated Halanay delay differential inequality[1]. Using this inequality, Liapunov function and vector Liapunov function, we show that our result can be applied to the stability behavior of solutions of some delay differential systems. And also, we attempt to relax some restrictions of dv/dt, which is necessary under Liapunov function's method on the delay differential systems.
基金Supported by the National Fund of Natural Sciences.
文摘In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery problem for such differential operator is considered.
文摘In this paper,making use of upper and lower solutions,we first prove the existence of the solu tion for integral differential equation of Volterra type.Then applying the theory of differential in equalities obtained,under the appropriate assumptions,by constructing the special function of upper and lower solutions,we demonstrate the existence of the solution for singularly preturbed integral differential equation of Volterra type,and give the uniformly valid approximate estimation.
基金Supported by the National Natural Science Foundation of China(10061004) Supported by the Natural Sciences Foundation of Yunnan province(2003A0001M)
文摘By using some differential inequality, a second-order delay differential equation(r(t)x′(t))′ + p(t)x(q(t)) = 0has been investigated and some necessary condition for this equation has a nonoscillatorysolution and some sufficient condition which ensures that all of the solutions of the aboveequation are oscillatory are obtained.
基金Supported by the National Natural Science Foundation of China (No. 10471039)the Natural Science Foundations of Zhejiang (No Y604127)Supported in part by E-Institutes of Shanghai Municipal Education Commission (No.E03004).
文摘In this paper, using the theory of differential inequalities, we study the nonlinear boundary value problem for a class of integro-differential system. Under appropriate assumptions, the existence of solution is proved and the uniformly valid asymptotic expansions for arbitrary n-th order approximation and the estimation of remainder term are obtained simply and conveniently.
文摘In this paper, the boundary value problem of quasilinear differential equation with two parameters is studied via differential inequalities. The asymptotic solution is found and the remainders is estimated.
文摘In this paper,we study the singular perturbation of boundary value problem of systems for quasilinear ordinary differential equations:x'=j(i,x,y,ε),εy'=g(t,x,y,ε)y'+h(t,x,y,ε),y(0,ε)=A(ε),y(0,ε)=B(ε),y(1,ε)=C(ε)where xf.y,h,A,B and C belong to Rn and a is a diagonal matrix.Under the appropriate assumptions,using the technique of diagonalization and the theory of differential inequalities we obtain the existence of solution and its componentwise uniformly valid asymptotic estimation.
基金Research supported by the National Natural Science Foundation of China (19971004 19871005).
文摘In this paper, positiveness theorems of solutions for several differential inequalities are proved and are used to prove the existence of traveling wave front solutions of reaction-diffusion systems. As an application, two examples are given.
基金The project is supported by Nature Science Foundation of Anhui Province Education Commission!( 98JL 1 2 9)
文摘In this paper,a kind of boundary value problems for Volterra functional differential equation is studied.\$\$εx″(t)=f(t,x(t),\(t),x(t-τ),x′(t),ε),t∈(0,1), x(t)=φ(t,ε),t∈[-τ,0], ax(1)+bx′(1)=A(ε).\$\$\ \ By using the theory of differential inequality,the author proves the existence of the solutions and a uniformly valid asymptotic expansion of the solution is given as well.
基金supported by NNSF of China(11671101)the National Science Center of Poland Under Maestro Advanced Project(UMO-2012/06/A/ST1/00262)Special Funds of Guangxi Distinguished Experts Construction Engineering
文摘In this paper,we consider a new differential variational inequality（DVI,for short）which is composed of an evolution equation and a variational inequality in infinite Banach spaces.This kind of problems may be regarded as a special feedback control problem.Based on the Browder＇s theorem and the optimal control theory,we show the existence of solutions to the mentioned problem.
基金supported by the National Natural Science Foundation of China(11301359,11171237)the Key Program of NSFC(70831005)
文摘In this article, a new differential inverse variational inequality is introduced and studied in finite dimensional Euclidean spaces. Some results concerned with the linear growth of the solution set for the differential inverse variational inequalities are obtained under different conditions. Some existence theorems of Caratheodory weak solutions for the differential inverse variational inequality are also established under suitable conditions. An application to the time-dependent spatial price equilibrium control problem is also given.
基金supported by the National Natural Science Foundation of China(11471230,11671282)。
文摘This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space.Utilizing the KKM theorem,a result concerned with the upper semicontinuity and measurability of the solution set of a hemivariational inequality is established.By using a fixed point theorem for a condensing setvalued map,the nonemptiness and compactness of the set of mild solutions are also obtained for such a system under mild conditions.Finally,an example is presented to illustrate our main results.
文摘In this paper we proved the A(p)-weighted inequalities for martingale transforms and differential subordinations of Banach-space-valued regular maringales. We discussed the relations between the weighted inequalities, A(p)-weight functions and the Banach spaces which has the UMD property or are isomorphic to Hilbert space.
基金supported by the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement(823731CONMECH)supported by National Natural Science Foundation of China(11671101),supported by National Natural Science Foundation of China(11961074)+2 种基金Guangxi Natural Science Foundation(2021GXNSFAA075022)Project of Guangxi Education Department(2020KY16017)Yulin normal university of scientific research fund for high-level talents(G2019ZK39,G2021ZK06)。
文摘We consider a differential variational-hemivariational inequality with constraints,in the framework of reflexive Banach spaces.The existence of a unique mild solution of the inequality,together with its stability,was proved in[1].Here,we complete these results with existence,uniqueness and convergence results for an associated penalty-type method.To this end,we construct a sequence of perturbed differential variational-hemivariational inequalities governed by perturbed sets of constraints and penalty coefficients.We prove the unique solvability of each perturbed inequality as well as the convergence of its solution to the solution of the original inequality.Then,we consider a mathematical model which describes the equilibrium of a viscoelastic rod in unilateral contact.The weak formulation of the model is in a form of a differential variational-hemivariational inequality in which the unknowns are the displacement field and the history of the deformation.We apply our abstract penalty method in the study of this inequality and provide the corresponding mechanical interpretations.
基金supported by the National Natural Science Foundation of China(11772306)Natural Science Foundation of Guangxi Province(2018GXNSFAA281021)+2 种基金Guangxi Science and Technology Base Foundation(AD20159017)the Foundation of Guilin University of Technology(GUTQDJJ2017062)the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(CUGGC05).
文摘This paper investigates the nonemptiness and compactness of the mild solution set for a class of Riemann-Liouville fractional delay differential variational inequalities,which are formulated by a Riemann-Liouville fractional delay evolution equation and a variational inequality.Our approach is based on the resolvent technique and a generalization of strongly continuous semigroups combined with Schauder's fixed point theorem.
基金NSF of Guangxi(Grant No.2023GXNSFAA026085)Guangxi Science and Technology Department Specific Research Project of Guangxi for Research Bases and Talents(Grant No.AD23023001)+1 种基金NNSF of China Grant Nos.12071413,12111530282 the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement No.823731 CONMECHthe Innovation Project of Guangxi University for Nationalities(Grant No.gxun-chxps202072)。
文摘The goal of this paper is to deal with a new dynamic system called a differential evolution hemivariational inequality(DEHVI)which couples an abstract parabolic evolution hemivariational inequality and a nonlinear differential equation in a Banach space.First,by apply ing surjectivity result for pseudomonotone multivalued mappins and the properties of Clarke's subgradient,we show the nonempty of the solution set for the parabolic hemivariational inequality.Then,some topological properties of the solution set are established such as boundedness,closedness and convexity.Furthermore,we explore the upper semicontinuity of the solution mapping.Finally,we prove the solution set of the system(DEHVI)is nonempty and the set of all trajectories of(DEHVI)is weakly compact in C(I,X).
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 Natural Science Foundation of Zhejiang Provivce (102009)Supported by the Natural Foundation of Huzhou Teacher's College(200302)
文摘In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solution is proved and the uniformly valid asymptotic expansions is obtained as well.
