受迫Liénard方程周期解的存在性

Existence of Periodic Solution to a Forced Liénard Equation

摘要:

对于受迫Liénard方程,利用Sobolev空间范数,给出了周期解的估计,进而利用变分原理、Schauder不动点定理,证明了周期解的存在性。

关键词:Lié;nard方程;临界点;Schauder不动点定理;全连续算子

Abstract:

To a forced Liénard equation discussed in this paper,the estimates of the periodic solution are given by using the norm estimate in the Sobolev space,then by virtue of the variation principle and Schauder's fixed point theorem,the existence of the periodic solution is proved.

Key words:Lié;nard equation;critical point;Schauder's fixed point theorem;completely continuous operator