Lienard方程周期解、概周期解的存在性

本文考虑 Lienard方程 x″+f (x) x′+g(x) =e(t) ,我们得到 :当 -∞ 0且 0

Existence of Periodic Solution or Almost Periodic Solution for Lienard Equation

In this paper, we consider the following equation x″+f(x)x′+g(x)=e(t)( a ) We obtained that equation (a) has periodic solution or almost periodic solution if -∞< inf x∈Rg′(x)≤ sup x∈Rg′(x)<0 , sup x∈R｜f(x)｜< +∞ and e(t) to be periodic or almost periodic function. Also for Lienard equation x″+f(x)x′+cx=e(t) (b) We obtained that equation (b) has periodic solution or almost periodic solution if C>0, 0< inf x∈R｜f(x)｜≤ sup x∈R｜f(x)｜< +∞ ,and e(t) to be periodic or almost periodic function.