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。     

退化时滞微分方程的周期解问题

本文讨论退化时滞微分方程的周期解问题．特别地，我们给出二维退化滞后微分方程的周期解的存在性问题，并在最后举例说明其应用。     

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。     

二阶多时滞非线性微分方程的周期解

研究二阶系数非线性多时滞微分方程ω周期解的存在性，得到了ω周期解存在的充分条件。     

中立型泛函微分方程的周期解

对于中立型泛函微分方程,证明了解的毕竟有界性蕴含周期解的存在性,把常微分方程中著名的Yoshizawa周期解存在定理推广到中立型泛函微分方程,然后利用所得结果给出一类产生于电力系统的中立型时滞泛函微分方程周期解存在惟一与吸引的条件。     

Banach空间半线性发展方程的周期解

把上、下解方法引入到有序Ｂａｎａｃｈ空间中的半线性发展方程周期解问题，利用正算子半群特征与单调迭代程序，获得了最大周期解与最小周期解的存在性．所得的结果概括和推广了常微分方程与偏微分方程中的有关结论     

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.     

Yoshizawa周期解定理的推广

证明了有限时滞系统解的毕竟有界性蕴含周期解的存在性，把常微分方程的相应结果推广到了泛函数微分方程。     

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.     

一类时滞脉冲微分方程的概周期解的存在性

运用锥上的不动点定理，研究一类脉冲时滞微分方程的概周期解，得到了保证系统存在概周期解的一组充分条件。     

Stability of Periodic Solutions of Ordinary Differential Equations in Banach Spaces

§１．ＤｅｆｉｎｉｔｉｏｎｓａｎｄＮｏｔａｔｉｏｎｓＬｅｔＥｂｅａｒｅａｌＢａｎａｃｈｓｐａｃｅ,ａｎｄｌｅｔｘ,ｙ∈Ｅ．Ｔｈｅｄｉｒｅｃｔｉｏｎａｌｄｅｒｉｖａｔｉｖｅ［ｘ,ｙ］－ｏｆｘａｎｄｙｉｓｄｅｆｉｎｅｄｂｙ（ｆｏｒｍｏｒｅｄｅｔａｉｌｓｓ...     

On the existence of periodic solutions of ordinary differential equations with high-frequency summands in a Banach space

Mathematical Notes - The question of the existence of periodic solutions of linear ordinary differential equations with high-frequency summands in a Banach space is studied.     

空间中高阶常微分方程周期边值问题的解的存在性(英文)

利用单调迭代方法 ,本文获得了 Banach空间中高阶常微分方程周期边值问题的解的存在性结果 ,推广了文 [3 ]中对应结果     

Asymptotic behavior of periodic dynamical systems on banach spaces

Summary The concept of a periodic dynamical system on a Banach space is a generalization of periodic ordinary, functional, and partial differential equations. A theory is presented which analyzes the asymptotic behavior of such systems in the spirit of the direct method of Liapunov. This research was supported by the United States Army under contract DA-31-124-ARO-D-270. Entrata in Redazione il 1 febbraio 1970.     

Banach空间中二阶非线性常微分方程周期边值问题

在Banach空间中利用上下解方法与增算子不动点定理，研究了含间断项的二阶非线性常微分方程周期边值问题的最大解、最小解的存在性，推广和改进了现有的结果．     

Banach空间中含间断项的二阶非线性常微分方程周期边值问题

在Banach空间中利用上下解方法与不连续增算子不动点定理，研究了含间断项和右端函数具有一阶导数项的二阶非线性常微分方程周期边值问题的最大解、最小解的存在性，推广和改进了现有的结果．而且对于有限维空间，我们获得的这些结果也都是新的．     

Existence of Almost Periodic Solutions for Jumping Discontinuous Systems

An existence result for almost periodic sequences of ordinary differential equations with linear boundary value conditions is derived by using the Banach fixed point theorem together with a method of majorant functions. An application is given to a damped pendulum with a jumping length and external force.     

Stability of Positive Fixed Points of Nonlinear Operators

This paper considers the stability of positive fixed points of nonlinear operators under purturbations. Through the use of the Thompson's metric, we obtain the results in ordered Banach spaces by proving the corresponding results in metric spaces first. An application to the existence of periodic solutions for a parametrized system of ordinary differential equations is given.     

Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C₀-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations.