Periodic solutions of second-order differential inclusions systems with \(p(t)\)-Laplacian (Q1938209)

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