In this paper,we try to discuss the conjecture which says that infinitesimal Ⅱ-isome try of surface is infintesimal Ⅰ -isometry. i. e, infinitesimal rigid.Under some weakly suppositions of Guass curvature,some new ...In this paper,we try to discuss the conjecture which says that infinitesimal Ⅱ-isome try of surface is infintesimal Ⅰ -isometry. i. e, infinitesimal rigid.Under some weakly suppositions of Guass curvature,some new results are worked out They are generalizations of known theories.展开更多
The problem of periodic solutions for Lienard equations with infinite delay x+(?)x+g(t,xt)=p(t)is discussed by using Mawhin's,coincidence degree theory. Some new results on the existence of periodic solutions are ...The problem of periodic solutions for Lienard equations with infinite delay x+(?)x+g(t,xt)=p(t)is discussed by using Mawhin's,coincidence degree theory. Some new results on the existence of periodic solutions are derived.展开更多
In this paper,the authors primarily explore a delayed competitor-competitor-mutualist Lotka-Volterra model,which is a system of differential equation with infinite integral.The authors first study the existence of pos...In this paper,the authors primarily explore a delayed competitor-competitor-mutualist Lotka-Volterra model,which is a system of differential equation with infinite integral.The authors first study the existence of positive periodic solutions of the model by using the Krasnoselskii's fixed point theorem,and then present an example to illustrate the main results.展开更多
This paper is concerned with the fault detection（FD） problem for a class of discretetime stochastic systems with channel fadings, randomly occurring multiple communication delays,and infinitely distributed delays. A...This paper is concerned with the fault detection（FD） problem for a class of discretetime stochastic systems with channel fadings, randomly occurring multiple communication delays,and infinitely distributed delays. All of the three phenomena have the characteristics of randomly occurring and three sequences of stochastic variables which are mutually independent but obey the Bernoulli distribution are employed to describe them. The aim of this paper is to design an FD filter such that the FD dynamics is exponentially stable in the mean square and, at the same time, the error between the residual signal and the fault signal is made as small as possible. Intensive analysis is utilized to derive the sufficient conditions for the designed FD filter, which guarantees the exponential stability and the prescribed H∞ performance. FD filter parameters are obtained by solving a convex optimization problem. An illustrative example is provided to demonstrate the effectiveness of the FD design scheme.展开更多
The authors study the existence of homoclinic type solutions for the following system of diffusion equations on R × RN：{atu-xu ＋ b ·▽xu ＋ au ＋ V（t,x）v = Hv（t,x,u,v）,-atv-xv-b·▽xv ＋ av ＋ V（...The authors study the existence of homoclinic type solutions for the following system of diffusion equations on R × RN：{atu-xu ＋ b ·▽xu ＋ au ＋ V（t,x）v = Hv（t,x,u,v）,-atv-xv-b·▽xv ＋ av ＋ V（t,x）u = Hu（t,x,u,v）,where z =（u,v）：R × RN → Rm × Rm,a 〉 0,b =（b1,···,bN） is a constant vector and V ∈ C（R × RN,R）,H ∈ C1（R × RN × R2m,R）.Under suitable conditions on V（t,x） and the nonlinearity for H（t,x,z）,at least one non-stationary homoclinic solution with least energy is obtained.展开更多
In this paper, a generalized impulsive model of hematopoiesis with infinite delays and linear harvesting term is investigated. The main purpose of this paper is to study the existence, uniqueness and exponential stabi...In this paper, a generalized impulsive model of hematopoiesis with infinite delays and linear harvesting term is investigated. The main purpose of this paper is to study the existence, uniqueness and exponential stability of the positive pseudo-almost periodic solutions, which improve and extend some known relevant results. Moreover, an example is given to illustrate the main findings.展开更多
文摘In this paper,we try to discuss the conjecture which says that infinitesimal Ⅱ-isome try of surface is infintesimal Ⅰ -isometry. i. e, infinitesimal rigid.Under some weakly suppositions of Guass curvature,some new results are worked out They are generalizations of known theories.
文摘The problem of periodic solutions for Lienard equations with infinite delay x+(?)x+g(t,xt)=p(t)is discussed by using Mawhin's,coincidence degree theory. Some new results on the existence of periodic solutions are derived.
基金supported by the National Natural Science Foundation of China under Grant No.11302002the Foundation of Outstanding Young Talent in University of Anhui Province of China under Grant No.2011SQRL022ZD
文摘In this paper,the authors primarily explore a delayed competitor-competitor-mutualist Lotka-Volterra model,which is a system of differential equation with infinite integral.The authors first study the existence of positive periodic solutions of the model by using the Krasnoselskii's fixed point theorem,and then present an example to illustrate the main results.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.61422301 and 61374127the Alexander von Humboldt Foundation of Germany and Youth Science Foundation of Daqing Normal University under Grant No.11ZR10
文摘This paper is concerned with the fault detection（FD） problem for a class of discretetime stochastic systems with channel fadings, randomly occurring multiple communication delays,and infinitely distributed delays. All of the three phenomena have the characteristics of randomly occurring and three sequences of stochastic variables which are mutually independent but obey the Bernoulli distribution are employed to describe them. The aim of this paper is to design an FD filter such that the FD dynamics is exponentially stable in the mean square and, at the same time, the error between the residual signal and the fault signal is made as small as possible. Intensive analysis is utilized to derive the sufficient conditions for the designed FD filter, which guarantees the exponential stability and the prescribed H∞ performance. FD filter parameters are obtained by solving a convex optimization problem. An illustrative example is provided to demonstrate the effectiveness of the FD design scheme.
基金Project supported by the National Natural Science Foundation of China (No.10971194)the Zhejiang Provincial Natural Science Foundation of China (Nos.Y7080008,R6090109)the Zhejiang Innovation Project (No.T200905)
文摘The authors study the existence of homoclinic type solutions for the following system of diffusion equations on R × RN：{atu-xu ＋ b ·▽xu ＋ au ＋ V（t,x）v = Hv（t,x,u,v）,-atv-xv-b·▽xv ＋ av ＋ V（t,x）u = Hu（t,x,u,v）,where z =（u,v）：R × RN → Rm × Rm,a 〉 0,b =（b1,···,bN） is a constant vector and V ∈ C（R × RN,R）,H ∈ C1（R × RN × R2m,R）.Under suitable conditions on V（t,x） and the nonlinearity for H（t,x,z）,at least one non-stationary homoclinic solution with least energy is obtained.
基金Acknowledgments This research is supported by the National Natural Science Foundation of China （Grant Nos. 11501507, 11426201, 61273016） and the Natural Science Foundation of Zhejiang Province （Grant No. LQ13A010015）.
文摘In this paper, a generalized impulsive model of hematopoiesis with infinite delays and linear harvesting term is investigated. The main purpose of this paper is to study the existence, uniqueness and exponential stability of the positive pseudo-almost periodic solutions, which improve and extend some known relevant results. Moreover, an example is given to illustrate the main findings.
