A Periodic Solution of the Generalized Forced Liénard Equation

Abstract

We consider the generalized forced Liénard equation as follows: ${({\varphi }_p(x^{\mathrm{\prime }}))}^{\mathrm{\prime }}+(f(x)+k(x)x^{\mathrm{\prime }})x^{\mathrm{\prime }}+g(x)=p(t)+s$. By applying Schauder's fixed point theorem, the existence of at least one periodic solution of this equation is proved.