A necessary and sufficient condition for existence and uniqueness of periodic solutions for a p-Laplacian Liénard equation

摘要

In this work, we investigate the following $p$-Laplacian Liénard equation: $$ (arphi_{p}(x'(t)))'+f(x(t))x'(t)+g(x(t))=e(t). $$ Under some assumption, a necessary and sufficient condition for the existence and uniqueness of periodic solutions of this equation is given by using Manásevich--Mawhin continuation theorem. Our results improve and extend some known results.