Almost periodic type solutions of differential equations with piecewise constant argument via almost periodic type sequences

The existence of almost periodic, asymptotically almost periodic, and pseudo almost periodic solutions of differential equations with piecewise constant argument is characterized in terms of almost periodic, asymptotically, and pseudo almost periodic sequences. Thus Meisters's and Opial's theorems are extended.     

带梯度算子二阶方程的渐近概周期解

利用渐近概周期函数的性质得到带梯度算子二阶方程的渐近概周期解在C（R^-）中的存在性．同时利用迭代法和线性常微分方程的概周期解的存在性和唯一性,得到R上此方程渐近概周期解的存在和唯一性．     

ASYMPTOTICALLY MEAN ALMOST PERIODIC SOLUTIONS TO RANDOM DIFFERENCE EQUATIONS

In this paper,we first investigate some basic properties of asymptotically mean almost periodic random sequences on Z + and then show some properties of asymptotically mean almost periodic solutions to random difference equations.     

一类非自治随机微分方程的均方渐近概周期解

本文研究了一类在可分Hilbert空间中的非自治随机微分方程的均方渐近概周期解.利用"Acquistapace-Terreni"条件,开方族和Banach不动点原理讨论了该类随机微分方程的均方渐近概周期解的存在唯一性,推广了该类随机微分方程的均方概周期解的存在唯一性问题.     

Asymptotic periodicity and almost automorphy for a class of Volterra integro‐differential equations

This work deals with the existence of asymptotically periodic (resp. asymptotically almost automorphic) solutions for a class of Volterra integro‐differential equations. As application, we examine sufficient conditions for the existence of asymptotically periodic (resp. asymptotically almost automorphic) mild solutions of an equation arising in the study of heat conduction in materials with memory. Copyright © 2012 John Wiley & Sons, Ltd.     

Asymptotically almost periodic,almost periodic and pseudo-almost periodic mild solutions for neutral differential equations

In this paper we establish the existence and uniqueness of almost periodic, asymptotically almost periodic and pseudo-almost periodic mild solutions for neutral differential equations in Banach spaces.     

Almost periodic solutions of discrete Volterra equations

For discrete Volterra equations with or without delay, we obtain several results concerning almost periodic solutions and asymptotically almost periodic solutions under certain conditions. We also investigate the relations among solutions of equations discussed and give an example to illustrate our results.     

Almost Periodic Solutions of Abstract Retarded Functional Differential Equations with Unbounded Delay

We establish the existence of bounded, almost periodic and asymptotically almost periodic mild solutions for first- and second-order abstract-retarded functional differential equations with unbounded delay.     

Asymptotically almost periodic and almost periodic solutions for partial neutral differential equations

In this work we study the existence of almost periodic and asymptotically almost periodic solutions for partial neutral functional differential equations with unbounded delay.     

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.     

On the Poincaré theorem with asymptotically periodic coefficients

We consider the case where the Poincaré theorem for difference equations with asymptotically constant coefficients is generalized to systems of difference equations with asymptotically periodic coefficients. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 9, pp. 1262–1267, September, 1998.     

Periodic and asymptotically periodic solutions of systems of nonlinear difference equations with infinite delay

In this paper we study the existence of periodic and asymptotically periodic solutions of a system of nonlinear Volterra difference equations with infinite delay. By means of fixed point theory, we furnish conditions that guarantee the existence of such periodic solutions.     

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．     

Asymptotic Behavior of Solutions of Nonlinear Difference Equations with Continuous Argument

We establish conditions for the existence and uniqueness of continuous asymptotically periodic solutions of nonlinear difference equations with continuous argument.     

Asymptotically almost periodic solutions of abstract retarded functional differential equations of second order

We establish existence of asymptotically almost periodic mild solutions for a class of semi-linear second-order abstract retarded functional differential equations with infinite delay.     

Perturbation of Volterra Difference Equations

A fixed point theorem is used to investigate nonlinear Volterra difference equations that are perturbed versions of linear equations. Sufficient conditions are established to ensure that the stability properties of linear Volterra difference equations are preserved under perturbation. The existence of asymptotically periodic solutions of perturbed Volterra difference equations is also proved.     

Periodic orbits of delay differential equations under discretization

This paper deals with the long-time behaviour of numerical solutions of delay differential equations that have asymptotically stable periodic orbits. It is shown that Runge-Kutta discretizations of such equations have attractive invariant curves which approximate the periodic orbit with the order of the method. The research by this author has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences.     

Asymptotically almost periodic solutions of abstract retarded functional differential equations of first order

We establish the existence of asymptotically almost periodic mild solutions for a class of semi-linear first-order abstract retarded functional differential equations with infinite delay.     

Existence of asymptotically almost periodic solutions for some second-order hyperbolic integrodifferential equations

Semigroup Forum - In this paper we study and obtain the existence of asymptotically almost periodic solutions to some classes of second-order hyperbolic integrodifferential equations of...     

Contributions to coincidence degree theory of asymptotically homogeneous operators

In this paper we give contributions to the coincidence degree theory of asymptotically homogeneous operators. Applications are given to the periodic problem for second-order functional differential equations.