Banach空间非线性发展方程的耦合周期解

本文利用上下解方法与正算子半群理论,讨论了Banach空间中具有混合单调（混拟单调）性质的非线性发展方程耦合周期解的存在性及周期解的存在唯一性,所得结果概括并推广了有关常微分方程和偏微分方程的若干结论．     

二阶非线性常微分方程的正周期解

本文应用Ｋｒａｓｎｏｓｅｌｓｋｉｉ锥映射不动点定理，研究了二阶非线性常微分方程的ω-周期解的存在性，获得了若干正ω-周期解的存在性与多重性结果．     

有序Banach空间中常微分方程正周期解的存在性

讨论了有序Banach空间E中的非线性常微分方程:u′(t)+Mu(t)=f(t,u(t)),(?)t∈R正ω-周期解的存在性,其中f:R×P→P连续,P为E中的正元锥.通过新的非紧性测度的估计技巧与凝聚映射的不动点指数理论获得了该问题正ω-周期解的存在性结果.     

YoshiZawa型周期解定理和Massera型周期解定理研究进展简介

微分方程解的有界性和周期解的存在性是檄分方程理论研究中的两个重要课题，二者之间有着紧密的联系．在解的有界性与周期解的存在性的研究中，Yoshizawa周期解定理和Massera周期解定理是非常重要的结果，具有重要的理论意义和应用价值．本文以Yoshizawa型周期解定理和Massera型周期解定理的研究为主，简要介绍泛函微分方程周期解理论研究方面的一些新进展。     

非自治时滞微分方程正周期解的存在性

应用Krasnoselskii锥映射不动点定理，研究了具一般时滞非线性非自治Logistic方程的ω-周期解的存在性，获得了存在正周期解的充分条件．     

具有比率型功能反应的时标动力学系统的周期解

研究了一类具有比率型功能反应的食物链时标动力学系统,利用重合度理论中的延拓定理讨论了此系统周期解的存在性问题,得到了保证周期解存在的充分条件,从而使这一类系统的连续与离散情形:微分方程和差分方程的周期解存在性问题得到了统一研究.     

滞后型脉冲泛函微分方程周期解的存在性

本文借助Mawhin重合度理论中的延拓定理和广义常微分方程周期解的存在性,在滞后型脉冲泛函微分方程与广义常微分方程存在等价关系的条件下,建立了滞后型脉冲泛函微分方程周期解的存在性定理.     

弱概周期微分方程的弱概周期解

本文利用微分方程的指数型三分性给出了弱概周期微分方程的弱概周期解的存在性定理,并讨论了弱概周期微分方程的一些性质,从而改进了文献[2—7]中的一些结果.     

强平均解与概周期解的存在性

本文定义了概周期微分方程的强平均解,利用强平均解的性质,讨论了强平均解与概周期解的关系,从而建立了概周期解存在的若干定理。     

一类具有无穷多个周期解的二阶偏微分方程

本文首先给出了一类具有无穷多个周期解的无阻尼二阶线性偏微分方程所描述的系统。同时讨论了一类无阻尼非线性二阶偏微分方程存在多个周期解的情况，最后给出了一个判断有阻尼二阶偏微分系统存在周期解的方法。     

关于退化中立型微分方程的周期解

讨论了退化中立型微分方程的周期解问题,给出了周期解存在性的条件和二维退化中立型微分方程周期解存在的代数判据,并且举例说明了其应用.     

一类高维滞后型泛函微分方程的周期解

本文研究一类滞后型函数分方程的周期解问题，利用指数型二分性和不动点定理，在较广泛的条件下证明了该方程的周期解的存在性及唯一性，推广并改进了文[1-3]的主要结果     

Systems of matrix rational differential equations arising in connection with linear stochastic systems with Markovian jumping

In this paper, a class of systems of matrix nonlinear differential equations containing as particular cases the systems of coupled Riccati differential equations arising in connection with control of some linear stochastic systems is considered.The system of differential equations considered in this paper are converted in a suitable nonlinear differential equation on a finite-dimensional Hilbert space adequately choosen.This allows us to use the positivity properties of the linear evolution operator defined by the linear differential equations of Lyapunov type.Our aim is to investigate properties of stabilizing and bounded solutions of the considered differential equations and to obtain some conditions ensuring the existence of such solutions.Conditions providing the existence of a maximal solution (minimal solution respectively) with respect to some classes of global solutions are presented. It is shown that if the coefficients of the equations are periodic functions all these special solutions (stabilizing, maximal, minimal) are periodic functions, too.Whenever possible the probabilistic arguments were avoided and so the results proved in the paper appear as results in the field of differential equations with interest in themselves.     

一类非线性微分方程渐近概周期解的存在性

利用函数的遍历性和耗散型条件,研究一类非线性微分方程渐近概周期解的存在性．在某些特定的条件下,得到了这类方程渐近概周期解存在性和唯一性结论．从而得到的结果在一定程度上推广和改进了相关结果．     

逐段常变量微分方程组概周期型解存在唯一性

通过差分方程指数二分法,我们研究了一类具有变系数逐段常变量微分方程组概周期与伪概周期解的存在唯一性与渐近稳定性,改进了已有文献的结果,并且得到了差分方程满足指数二分性的一个充分条件．     

Differential equations with limit-periodic forcings

The present paper is concerned with scalar differential equations of first order which are limit periodic in the independent variable. Some tools provided by the theories of exponential dichotomies and periodic differential equations are applied to prove that, in a generic sense, the existence of a bounded solution implies the existence of a limit periodic solution.

     

Existence of weighted pseudo almost periodic solutions to some classes of hyperbolic evolution equations

This paper is concerned with the study of weighted pseudo almost periodic solutions to some classes of hyperbolic differential equations. Upon making some suitable assumptions, the existence and uniqueness of a weighted pseudo almost periodic solution is obtained. To illustrate our main result, we study the existence of a weighted pseudo almost periodic solution to a system of partial differential equations arising in control systems described by abstract retarded functional-differential equations with feedback control.     

On the spectrum of almost periodic solution of second-order differential equations with piecewise constant argument

We study the spectrum containment of almost periodic solution to second order differential equations with piecewise constant argument. Some known (periodic, quasi-periodic) results would be expanded. As a corollary, it is shown that such equations with periodic perturbations possess a quasi-periodic solution and no periodic solution. This phenomena is due to the piecewise constant argument. The results are extended to nonlinear equations.     

On the module containment of the almost periodic solution for a class of differential equations with piecewise constant delays

In the first part of this paper, we obtain a new property on the module containment for almost periodic functions. Based on it, we establish the module containment of an almost periodic solution for a class of differential equations with piecewise constant delays. In the second part, we investigate the existence, uniqueness and exponential stability of a positive almost periodic and quasi-periodic solution for a certain class of logistic differential equations with a piecewise constant delay. The module containment for the almost periodic solution is established.