Periodic Solutions of Second-Order Differential Inclusions Systems with p ( t ) -Laplacian

Abstract

The existence of periodic solutions for nonautonomous second-order differential inclusion systems with $p(t)$-Laplacian is considered. We get some existence results of periodic solutions for system, $(d/dt)({|\dot{u}(t)|}^{p(t)-2}\dot{u}(t))\in \partial F(t,u(t))$ a.e. $t\in [0,T]$, $u(0)-u(T)=\dot{u}(0)-\dot{u}(T)=0$, by using nonsmooth critical point theory. Our results generalize and improve some theorems in the literature.