Limit Cycles of Liénard Systems with Several Equilibria

Abstract

In the paper we generalize some classic results on limit cycles of Liénard system

$$\dot{x}=\phi(y)-F(x),\quad\dot{y}=-g(x)$$

having a unique equilibrium to that of the system with several equilibria. As applications, we strictly prove the number of limit cycles and obtain the distribution of limit cycles for three classes of Liénard systems, in which we correct a mistake in the literature.