In this paper, the existence of almost periodic solutions to general BAM neural networks with leakage delays on time scales is first studied, by using the exponential dichotomy method of linear differential equations ...In this paper, the existence of almost periodic solutions to general BAM neural networks with leakage delays on time scales is first studied, by using the exponential dichotomy method of linear differential equations and fixed point theorem. Then, the exponential stability of almost periodic solutions to such BAM neural networks on time scales is discussed by utilizing differential inequality. Finally, an example is given to support our results in this paper and the results are up-to-date.展开更多
In this paper, the existence and uniqueness of almost periodic solutions for some infinite delay integral equations are discussed. By using Krasnoselskii fixed point theorem,some new results are obtained.
This paper deals with the problems on the existence and uniqueness and stability of almost periodic solutions for functional differential equations with infinite delays.The author obtains some sufficient conditions wh...This paper deals with the problems on the existence and uniqueness and stability of almost periodic solutions for functional differential equations with infinite delays.The author obtains some sufficient conditions which ganrantee the existence and uniqueness and stability of almost periodic solutions with module containment.The results extend all the results of the paper and solve the two open problems proposed in under much weaker conditions than that proposed in.展开更多
In this paper, we study the problems on the existence, uniqueness and stability of almost periodic solution for a class of nonlinear system. Using fixed point theorem and Lyapunov functional, the sufficient conditions...In this paper, we study the problems on the existence, uniqueness and stability of almost periodic solution for a class of nonlinear system. Using fixed point theorem and Lyapunov functional, the sufficient conditions are given which guarantee the existence, uniqueness and stability of almost periodic solution for the system.展开更多
In this paper, we consider almost periodic discrete two-species competitive sys-tems. By using Lyapunov functional, the existence conditions and uniqueness of almost periodic solutions for the this type of systems are...In this paper, we consider almost periodic discrete two-species competitive sys-tems. By using Lyapunov functional, the existence conditions and uniqueness of almost periodic solutions for the this type of systems are obtained.展开更多
This paper studies equation x' + cx' + g(x) = P(t,x). Under some suitable conditions the existence and uniqueness of almost periodic solution of this equation are given.
By using the ordinary dichotomy and theory of stability, we study the nonlinear differential equation and obtain some sufficient conditions which guarantee the existence and stability of almost periodic solution for t...By using the ordinary dichotomy and theory of stability, we study the nonlinear differential equation and obtain some sufficient conditions which guarantee the existence and stability of almost periodic solution for the nonlinear differential equation.展开更多
This paper deals with an abstract periodic gradient system in which the gradient is taken with respect to a variable metric. We obtain an existence and uniqueness result via the application of a global inverse theorem.
In this paper,we consider the periodic solution problems for the systems with unbounded delay,and the existence,uniqueness and stability of the periodic solution are dealt with unitedly.First we establish the suitable...In this paper,we consider the periodic solution problems for the systems with unbounded delay,and the existence,uniqueness and stability of the periodic solution are dealt with unitedly.First we establish the suitable delay-differential inequality,then study seperately the problems of periodic solution for the systems with bounded delay,with unbounded delay and the Volterra integral-dlfferentlal systems with infinite delay by using the character of matrix measure and the asymptotic fixed point theorem of poincaré’s periodic operator in the different phase spaces.A series of simple criteria for the existence,uniqueness and stability of these systems are obtained.展开更多
In [1] and [2], the authors made a deep qualitative analysis of the equationwith the character of tangent detected phase and they mathematically provided atheoretical basis of why the phase looked loop has no look--lo...In [1] and [2], the authors made a deep qualitative analysis of the equationwith the character of tangent detected phase and they mathematically provided atheoretical basis of why the phase looked loop has no look--losing point. However,according to many practical experts, it is rather difficult to put such a phaselooked loop into practice, though it has fine properties. W. C. Lindsey [3] made a展开更多
In this paper, we study the following nonlinear biological modeldx(t)/dt = x(t)[a(t)-b(t)x α (t)] + f(t, xt),by using fixed pointed theorem, the sufficient conditions of the existence of unique positive almost period...In this paper, we study the following nonlinear biological modeldx(t)/dt = x(t)[a(t)-b(t)x α (t)] + f(t, xt),by using fixed pointed theorem, the sufficient conditions of the existence of unique positive almost periodic solution for the above system are obtained, by using the theories of stability, the sufficient conditions which guarantee the stability of the positive almost periodic solution are derived.展开更多
In this paper, we study the anti-periodic solutions for 2n-th order differential equations. By using the Schauder＇s fixed point theorem, we present some new results about the existence and uniqueness of anti-periodic...In this paper, we study the anti-periodic solutions for 2n-th order differential equations. By using the Schauder＇s fixed point theorem, we present some new results about the existence and uniqueness of anti-periodic solutions for 2n-th order differential equations.展开更多
In this paper, we study the problem of almost periodic solution for the cellular neural networks with variable coefficients and delays. By ingeniously importing real parameters di > 0(i = 1,2,…n) which can be adju...In this paper, we study the problem of almost periodic solution for the cellular neural networks with variable coefficients and delays. By ingeniously importing real parameters di > 0(i = 1,2,…n) which can be adjusted, we establish some sufficient conditions which ensure the neural networks exist a unique almost periodic solution, and all other solutions exponentially converge to such an almost periodic solution.展开更多
In the paper, we study the positive solutions of an elliptic system coming from a preypredator model with modified Leslie-Gower and Holling-Type II schemes. We study the existence, non-existence, bifurcation, uniquene...In the paper, we study the positive solutions of an elliptic system coming from a preypredator model with modified Leslie-Gower and Holling-Type II schemes. We study the existence, non-existence, bifurcation, uniqueness and stability of positive solutions. In particular, we obtain a continuum of positive solutions connecting a semitrivial solution to the unique positive solution of the limiting system.展开更多
A new fixed point theorem is presented and sufficient conditions are obtained for the existence, uniqueness and global attractivity of a positive almost periodic solution to a delayed differential equation with almost...A new fixed point theorem is presented and sufficient conditions are obtained for the existence, uniqueness and global attractivity of a positive almost periodic solution to a delayed differential equation with almost periodic factors.展开更多
The existence and uniqueness of a strong periodic solution of the evolution system describing geophysical flow in bounded domains of RN (N = 3, 4) are proven if external forces are periodic in time and sufficiently sm...The existence and uniqueness of a strong periodic solution of the evolution system describing geophysical flow in bounded domains of RN (N = 3, 4) are proven if external forces are periodic in time and sufficiently small.展开更多
In this paper,using fixed point method,we discuss the problem of periodic solution to a class of higher dimensional functional differential equation.Our results extend and improve some results of the previous researches.
This paper deals with the problems on the existence and uniqueness and stability of almost periodic solutions of a higher almost periodic system. We establish the sufficient conditions which guarantee the existence an...This paper deals with the problems on the existence and uniqueness and stability of almost periodic solutions of a higher almost periodic system. We establish the sufficient conditions which guarantee the existence and uniqueness and stability of almost periodic solutions of this system.展开更多
In this paper, we study some n dimensional nonautonomous Lotka-Volterra competitive ecological systems. We then obtain permanence of such systems, as well as the existence, uniqueness and global asymptotic stability o...In this paper, we study some n dimensional nonautonomous Lotka-Volterra competitive ecological systems. We then obtain permanence of such systems, as well as the existence, uniqueness and global asymptotic stability of almost periodic positive solutions to these systems.展开更多
The existence of an almost periodic solutions to a nonlinear delay diffierential equation is considered in this paper. A set of sufficient conditions for the existence and uniqueness of almost periodic solutions to so...The existence of an almost periodic solutions to a nonlinear delay diffierential equation is considered in this paper. A set of sufficient conditions for the existence and uniqueness of almost periodic solutions to some delay diffierential equations is obtained.展开更多
基金Partially supported by the Special Basic Cooperative Research Programs of Yunnan Provincial Undergraduate Universities'Association(Grant No.202101BA070001-045).
文摘In this paper, the existence of almost periodic solutions to general BAM neural networks with leakage delays on time scales is first studied, by using the exponential dichotomy method of linear differential equations and fixed point theorem. Then, the exponential stability of almost periodic solutions to such BAM neural networks on time scales is discussed by utilizing differential inequality. Finally, an example is given to support our results in this paper and the results are up-to-date.
基金supported by the National Natural Science Foundation of China（11371027） the Projects of Outstanding Young Talents of Universities in Anhui Province（gxyq2018116）+2 种基金 the Teaching Groups in Anhui Province（2016jxtd080,2015jxtd048） the NSF of Educational Bureau of Anhui Province（KJ2017A702,KJ2017A704） the NSF of Bozhou University（BZSZKYXM201302,BSKY201539）
文摘In this paper, the existence and uniqueness of almost periodic solutions for some infinite delay integral equations are discussed. By using Krasnoselskii fixed point theorem,some new results are obtained.
文摘This paper deals with the problems on the existence and uniqueness and stability of almost periodic solutions for functional differential equations with infinite delays.The author obtains some sufficient conditions which ganrantee the existence and uniqueness and stability of almost periodic solutions with module containment.The results extend all the results of the paper and solve the two open problems proposed in under much weaker conditions than that proposed in.
文摘In this paper, we study the problems on the existence, uniqueness and stability of almost periodic solution for a class of nonlinear system. Using fixed point theorem and Lyapunov functional, the sufficient conditions are given which guarantee the existence, uniqueness and stability of almost periodic solution for the system.
基金the Natural Science Foundation of Fujian Province (Z0511014)the Foundation of Developing Science and Technology of Fuzhou University (2005-QX-18, 2005-QX-21).
文摘In this paper, we consider almost periodic discrete two-species competitive sys-tems. By using Lyapunov functional, the existence conditions and uniqueness of almost periodic solutions for the this type of systems are obtained.
基金This work was supported by Fujian Education Department Science Foundation (K20009).
文摘This paper studies equation x' + cx' + g(x) = P(t,x). Under some suitable conditions the existence and uniqueness of almost periodic solution of this equation are given.
文摘By using the ordinary dichotomy and theory of stability, we study the nonlinear differential equation and obtain some sufficient conditions which guarantee the existence and stability of almost periodic solution for the nonlinear differential equation.
文摘This paper deals with an abstract periodic gradient system in which the gradient is taken with respect to a variable metric. We obtain an existence and uniqueness result via the application of a global inverse theorem.
文摘In this paper,we consider the periodic solution problems for the systems with unbounded delay,and the existence,uniqueness and stability of the periodic solution are dealt with unitedly.First we establish the suitable delay-differential inequality,then study seperately the problems of periodic solution for the systems with bounded delay,with unbounded delay and the Volterra integral-dlfferentlal systems with infinite delay by using the character of matrix measure and the asymptotic fixed point theorem of poincaré’s periodic operator in the different phase spaces.A series of simple criteria for the existence,uniqueness and stability of these systems are obtained.
文摘In [1] and [2], the authors made a deep qualitative analysis of the equationwith the character of tangent detected phase and they mathematically provided atheoretical basis of why the phase looked loop has no look--losing point. However,according to many practical experts, it is rather difficult to put such a phaselooked loop into practice, though it has fine properties. W. C. Lindsey [3] made a
基金Supported by the NNSF of China(11171135)Supported by the Jiangsu Province Innovation Project of Graduate Education(1221190037)
文摘In this paper, we study the following nonlinear biological modeldx(t)/dt = x(t)[a(t)-b(t)x α (t)] + f(t, xt),by using fixed pointed theorem, the sufficient conditions of the existence of unique positive almost periodic solution for the above system are obtained, by using the theories of stability, the sufficient conditions which guarantee the stability of the positive almost periodic solution are derived.
文摘In this paper, we study the anti-periodic solutions for 2n-th order differential equations. By using the Schauder＇s fixed point theorem, we present some new results about the existence and uniqueness of anti-periodic solutions for 2n-th order differential equations.
基金This work was supported by Scientific research foundation of affairs concerning national living abroad office of the State Council.
文摘In this paper, we study the problem of almost periodic solution for the cellular neural networks with variable coefficients and delays. By ingeniously importing real parameters di > 0(i = 1,2,…n) which can be adjusted, we establish some sufficient conditions which ensure the neural networks exist a unique almost periodic solution, and all other solutions exponentially converge to such an almost periodic solution.
基金supported by National Natural Science Foundation of China (Grant Nos. 10471022, 10771032)Natural Science Foundation of Jiangsu Province (Grant No. BK2006088)
文摘In the paper, we study the positive solutions of an elliptic system coming from a preypredator model with modified Leslie-Gower and Holling-Type II schemes. We study the existence, non-existence, bifurcation, uniqueness and stability of positive solutions. In particular, we obtain a continuum of positive solutions connecting a semitrivial solution to the unique positive solution of the limiting system.
基金supported by the NNSF of China (10571064)the research Foundation of the Doctoral Program of Higher Education of China (20094407110001)the NSF of Guangdong Province (10151063101000003)
文摘A new fixed point theorem is presented and sufficient conditions are obtained for the existence, uniqueness and global attractivity of a positive almost periodic solution to a delayed differential equation with almost periodic factors.
基金the Special Funds for Major State Basic Research Projects of China(No.G1999032801) and the National Natural Science Foundation
文摘The existence and uniqueness of a strong periodic solution of the evolution system describing geophysical flow in bounded domains of RN (N = 3, 4) are proven if external forces are periodic in time and sufficiently small.
文摘In this paper,using fixed point method,we discuss the problem of periodic solution to a class of higher dimensional functional differential equation.Our results extend and improve some results of the previous researches.
文摘This paper deals with the problems on the existence and uniqueness and stability of almost periodic solutions of a higher almost periodic system. We establish the sufficient conditions which guarantee the existence and uniqueness and stability of almost periodic solutions of this system.
文摘In this paper, we study some n dimensional nonautonomous Lotka-Volterra competitive ecological systems. We then obtain permanence of such systems, as well as the existence, uniqueness and global asymptotic stability of almost periodic positive solutions to these systems.
文摘The existence of an almost periodic solutions to a nonlinear delay diffierential equation is considered in this paper. A set of sufficient conditions for the existence and uniqueness of almost periodic solutions to some delay diffierential equations is obtained.
