ON THE EXISTENCE OF LIMIT CYCLES OF LIENARD EQUATION

In this paper,we have proved several theorems which guarantee that the Lienardequation has at least one or n limit cycles without using the traditional assmuption G(±∞)=+∞.Thus some results in[3 -5]are extended.The limit cycles can be located by ourtheorems.Theorems3 and4 give sufficient conditions for the existence of n limit cycleshaving no need of the conditions that the function F(x)is odd or“nth order compatible witheach other”or“nth order contained in each other”.