Multiple periodic solutions of some Liénard equations with p-Laplacian

Abstract

The existence, non-existence and multiplicity of solutions to periodic boundary value problems of Liénard type \begin{eqnarray*} (|u'|^{p-2}u')'+ f(u)u'+ g(u) = e(t) + s,\quad u(0)-u(T)=0=u'(0)-u'(T), \end{eqnarray*} is discussed, where $p>1,$ $f$ is arbitrary and $g$ is assumed to be bounded, positive and $g(\pm\infty)=0.$ The function $e$ is continuous on $[0,T]$ with mean value $0$ and $s$ is a parameter.