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。     

一类二阶迭代泛函微分方程周期解的存在性

利用k-集压缩算子抽象连续性定理和一些分析技巧,研究了一类二阶迭代泛函微分方程周期解的存在性,得到了一些保证该类方程存在周期解的新结果.     

Existence and uniqueness of pseudo-almost periodic solutions to some classes of partial evolution equations

Some sufficient conditions for the existence and uniqueness of pseudo-almost periodic (mild) solutions to some classes of partial evolution equations are given. We then make use of our abstract results to discuss the existence of pseudo-almost periodic solutions to some partial differential equations.     

概周期解的存在性、唯一性与稳定性

本文给出了一些保证微分方程的周期解和概周期解的存在性、唯一性、稳定性与不稳定性的充分性条件及周期解的存在范围估计式.所得结果推广[1]的主要结果及[2-6]的有关结果.     

时标上具有阶段结构的三种群捕食系统的周期解

研究了时标上具有阶段结构的三种群捕食系统.运用时标上连续拓扑度定理,得到了系统存在周期解的充分条件.其研究方法使系统的连续时间情形和离散时间情形的周期解问题得到了统一,被广泛地应用来研究微分方程和差分方程的周期解的存在问题.     

一类泛函微分方程半正问题的正周期解

运用Krasnosel’skii不动点理论研究了一类含参泛函微分方程半正问题正周期解的存在性．获得了当参数充分小时正周期解的存在性结果以及半正问题正周期解存在的充分条件．丰富了一阶泛函微分方程解的存在性理论．     

Almost automorphic solutions for some partial functional differential equations

In this work, we study the existence of almost automorphic solutions for some partial functional differential equations. We prove that the existence of a bounded solution on R⁺ implies the existence of an almost automorphic solution. Our results extend the classical known theorem by Bohr and Neugebauer on the existence of almost periodic solutions for inhomegeneous linear almost periodic differential equations. We give some applications to hyperbolic equations and Lotka-Volterra type equations used to describe the evolution of a single diffusive animal species.     

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．     

无穷时滞Liénard方程的周期解

讨论具有无穷时滞Liénard型方程x+э2F(x)/эx2x+g(t,xt)=p(t)的周期解问题,利用重合度理论得到了周期解存在的充分条件.     

PERIODIC SOLUTIONS FOR HIGHER ORDER DELAY FUNCTIONAL DIFFERENTIAL EQUATION OF NEUTRAL TYPE WITH LINEAR RESTORING TERMS

Using the theory of coincidence degree, the authors studied the existence of periodic solutions for higher order delay functional differential equations of neutral type with restoring terms and some new results for the existence of periodic solutions have been obtained.     

EXISTENCE OF PERIODIC SOLUTION TO HIGHER ORDER DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENT

In this paper,using the coincidence degree theory of Mawhin,we investigate the existence of periodic solutions to higher order differential equations with deviating argument. Some new results on the existence of periodic solutions to the equations are obtained. In addition,we give an example to illustrate the main results.     

脉冲泛函微分方程的正周期解

运用Leray-Schauder不动点定理研究一类脉冲泛函微分方程的正周期解的存在性,获得了存在正周期解的充分条件,改进了已知文献中的结果.     

带脉冲的p-Laplacian系统的周期解研究

本文用变分法研究了一类带脉冲的p-Laplacian周期解的存在性问题.其中特别强调了脉冲效应,得到了由脉冲生成的解.特别地,非线性项可以取为零,当p=2时,我们的结果可以用来研究差分方程的周期解的存在性.     

Weighted pseudo-almost periodic solutions of a class of abstract differential equations

For abstract linear functional differential equations with a weighted pseudo-almost periodic forcing term, we prove that the existence of a bounded solution on R⁺ implies the existence of a weighted pseudo-almost periodic solution. Our results extend the classical theorem due to Massera on the existence of periodic solutions for linear periodic ordinary differential equations. To illustrate the results, we consider the Lotka-Volterra model with diffusion.     

EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR INFINITE DELAY FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper, the existence of positive periodic solutions for infinite delay functional differential equations(FDEs for short) is discussed by utilizing a fixed point theorem on a cone in Banach space. Some results on the existence of positive periodic solutions are derived.     

Variational approach to impulsive differential equations with periodic boundary conditions

In this paper, we obtain some new existence results of solutions of impulsive differential equations with periodic boundary conditions. The main tool that we use is critical point theory. Our results generalize some existing results on periodic solutions for second order ordinary differential equations even when the impulses are absent.     

Proof and generalization of Kaplan-Yorke’s conjecture under the condition f ' (0) > 0 on periodic solution of differential delay equations

Using the theory of existence of periodic solutions of Hamiltonian systems, it is shown that many periodic solutions of differential delay equations can be yielded from many families of periodic solutions of the coupled generalized Hamiltonian systems. Some sufficient conditions on the existence of periodic solutions of differential delay equations are obtained. As a corollary of our results, the conjecture of Kaplan-Yorke on the search for periodic solutions for certain special classes of scalar differential delay equations is shown to be true when . Project supported by the National Natural Science Foundation of China (Grant No. 19731003) and Science Foundation of Yunnan Province.     

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.     

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。     

一类时滞Logistic方程正周期解的存在性

In the present paper,we consider the existence of positive periodic solu-tions for a kind of delay Logistic equations.By using a fixed point theorem in cones,we give some new existence results of single and multiple positive periodic solutionsfor a kind of delay Logistic equations.Some biomathematical models are presentedto illustrate our results.