On the existence of periodic solutions for p-Laplacian generalized Liénard equation

Abstract

By employing Mawhin's continuation theorem, the existence of periodic solutions of the p-Laplacian generalized Liénard equation with deviating argument$\left({\varphi }_p\right(x^{\prime }\left(t\right)){)}^{\prime }+f(t,x\left(t\right)\left)x^{\prime }\right(t)+\beta (t\left)g\right(x(t-\tau (t\left)\right))=e(t)$under various assumptions are obtained.