一致最终有界性与具无限时滞非线性积分微分方程的周期解

摘要

在具有衰减记忆的允许相空间(Cg·|·|g)中,利用Horn不动点定理研究了具有无限时滞积分微分方程周期解的存在性.去掉了周期解定理中的“一致有界性”条件,得到方程解的一致最终有界性蕴含周期解的存在性,所得结果推广了已有的一些结论.%In this paper Horn's fixed-point theorem is used to study the existence of periodic solution of nonlinear integro-differential equations with infinite delay in the permissible phase space (C8· | · |8) which have fading memory. It has been proved that, the uniform ultimate bounded solutions implies the existence of periodic solutions and some known results are generalized.