广义Liénard系统闭轨的存在性

On the Existence of Closed Orbits for Generalized Lienard System

本文研究广义Liénard系统x=φ(y),y=-φ(y)f(x)-g(x)闭轨的存在性问题.获得了保证此系统存在闭轨的两组充分条件.在我们的定理中f(x)允许无限次变号,特别在我们的定理2中,去掉了以往关于Liénard系统极限环存在性结果中f(0)【0(或】0)的常设条件.

In this paper,we have studied the existence of closed orbits for the generalized Lienard system: x=φ(y), y=-φ(y)f(x)-g(x). Some sufficient conditions are established to ensure that the system has at least one closed orbit. In our theorems, we allow the sign of f(x) to change infinite times,particular, our theorem 2 gives the conditions under which the system has a closed orbit without the traditional assumption that f(0)<0(orf(0)>0).