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．     

具有阶段结构且食饵有避难所的模型分析

研究了捕食者具有阶段结构且食饵有避难所的非自治捕食系统.利用Lyapunov函数方法得到了系统持续生存的条件,以及在一定条件下存在唯一全局渐进稳定的周期正解.对于更广泛的概周期现象,也得到了存在唯一全局渐进稳定的概周期正解的充分条件.     

Positive periodic solution for a neutral delay competitive system

In this paper we study the existence of positive periodic solutions for a class of neutral type competitive system with delay. Applying the continuation theorem of coincidence degree theory, a general criteria on the existence of positive periodic solutions are established. Some the related results are generalized and improved. It is shown that the arguments delays have no effect on the existence positive periodic solution of system.     

高维时滞周期的Kolmogorov型系统的正周期解

本文应用Ｂａｎａｃｈ空间中的Ｈｏｒｎ不动点得到了高维时滞的周期Ｋｏｌｍｏｇｏｒｏｖ型生态系统的正周期解存在性定理,作为这个定理的应用,讨论了几类时滞的周期ＬｏｔｋａＶｏｌｔｅｒｒａ型系统的正周期解的存在性问题,建立了新的实用的判别准则。     

一类具第三类功能反应且食饵具有避难所的捕食系统的分析

研究了一类具第三类功能反应且食饵具有避难所的非自治捕食系统.利用Lyapunov函数方法得到了系统持续生存的条件,以及在一定条件下,系统存在全局渐进稳定的周期正解.对于更广泛的概周期现象,也得到了存在唯一全局渐进稳定的概周期正解的充分条件.     

EXISTENCE OF MULTIPLE POSITIVE PERIODIC SOLUTIONS TO A CLASS OF INTEGRO-DIFFERENTIAL EQUATION

In this paper,by the Avery-Henderson fixed point theorem,we investigate the existence of multiple positive periodic solutions to a class of integro-differential equation. Some suficient conditions are obtained for the existence of multiple positive periodic solutions.     

具有状态依赖时滞的脉冲微分的方程周期解的存在性

研究一类具状态依赖时滞的脉冲微分方程的周期解的存在性,利用锥不动点定理获得了关于周期解存在的一些结果.     

一类无穷时滞周期Lotka-Volterra型系统的正周期解

该文研究一类无穷时滞周期Ｌｏｔｋａ Ｖｏｌｔｅｒｒａ型系统正周期解的存在性．应用Ｓｃｈａｕｄｅｒ不动 点定理得到了一个比较一般的正周期解存在定理．文献［１,２］中的主要结果被改进和推广．     

Lazer–Leach type conditions on periodic solutions of semilinear resonant Duffing equations with singularities

In this paper, we study the existence of positive periodic solutions of resonant Duffing equations with singularities. Some Lazer–Leach type conditions are given to ensure the existence of positive periodic solutions of singular resonant Duffing equations.     

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.     

MULTIPLE PERIODIC SOLUTIONS TO SECOND ORDER FUNCTIONAL DIFFERENTIAL EQUATION WITH INFINITE DELAY

This paper is concerned with the existence of positive periodic solutions to a second order functional differential equation with infinite delay.Under the appropriate conditions,some existence and multiplicity of positive periodic solutions are derived by an abstract fixed-point theorem.     

ALMOST PERIODIC SOLUTIONS OF SINGLE POPULATION MODELS WITH ALMOST PERIODIC ENVIRONMENT

ＡＬＭＯＳＴＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＯＦＳＩＮＧＬＥＰＯＰＵＬＡＴＩＯＮＭＯＤＥＬＳＷＩＴＨＡＬＭＯＳＴＰＥＲＩＯＤＩＣＥＮＶＩＲＯＮＭＥＮＴＨｅＣｈｏｎｇｙｏｕ（ＮａｎｊｉｎｇＵｎｉｖｅｒｓｔｙ）（何崇佑）南京大学，邮编：２１０００８Ａｂ...     

Existence and exponential stability of positive almost periodic solutions for high-order Hopfield neural networks

This paper is concerned with the existence and exponential stability of positive almost periodic solutions of high-order Hopfield neural networks (HHNNs) with time-varying delays. Some sufficient conditions for the existence and exponential stability of positive almost periodic solutions are established.     

一类脉冲中立型多种群时滞微分方程正周期解的存在性

利用新的重合度理论中的连续性定理,给出了一类带有脉冲的中立型时滞微分方程的正周期解的存在性判定定理.     

A Landesman-Lazer type condition for second-order differential equations with a singularity at resonance

In this paper, we are concerned with the existence of positive periodic solutions for second-order differential equations with a singularity at resonance. A Landesman-Lazer type condition is given to obtain the existence of positive periodic solutions using phase-plane analysis method and topological degree method.     

Periodic solutions of a nonautonomous periodic model of population with continuous and discrete time

In this paper, we employ the Mawhin's continuation theorem to study the existence of positive periodic solutions of the nonautonomous periodic model of population with continuous and discrete time. It is interesting that the conditions to guarantee the existence of positive periodic solutions of discrete time model are similar to those for the corresponding continuous time model.     

On the existence of positive solutions for nonlinear differential equations with periodic boundary conditions

We prove the existence of positive solutions of second-order nonlinear differential equations on a finite interval with periodic boundary conditions and give upper and lower bounds for these positive solutions. Obtained results yield positive periodic solutions of the equation on the whole real axis, provided that the coefficients are periodic.     

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.     

一类具有收获率的脉冲Lotka-Volterra竞争合作系统的八个正概周期解

研究了一类具有收获率的脉冲Lotka-Volterra竞争合作系统的正概周期解.通过利用重合度理论延拓定理、概周期理论和不等式分析技巧,获得了系统至少存在8个正概周期解的充分条件,推广和改进了早期文献的相关结果.     

Positive periodic solutions of nonlinear differential systems with impulses

By using a fixed point theorem of strict-set-contraction, sufficient conditions for the existence of positive periodic solutions of nonlinear differential systems with impulses are obtained. As applications of our results, the existence of positive periodic solutions are established for delay Lotka–Volterra systems with impulses or without impulses.