时滞广义Lienard微分方程的概周期解的存在性和稳定性

The existence and asymptotical stability of the almost periodic solution of the generalized lienard differential equation with delay

文章运用二分性及压缩映射原理,研究一类时滞广义Lienard微分方程x″+[f(x(t-τ))+h(t)]x′+q(t)x+g(t,x(t-τ))=p(t)的概周期解的存在性和稳定性,得到此类微分方程的概周期解存在唯一性的充分性定理。

Using the theory of exponential dichotomy and the fixed point theorem,this paper studies the existence and stability of the almost periodic solution of the generalized Lienard system with delay x″+[f(x(t-τ))+h(t)]x′+e(t)x+g(t,x(t-τ))=p(t),and obtains the sufficient conditions of the existence of the uniformly asymptotically stable almost periodic solution for system.