Infinitely many solutions for a differential inclusion problem in

In this paper we consider the differential inclusion problem where is radially symmetric, and ∂F stands for the generalized gradient of a locally Lipschitz function . Under suitable oscillatory assumptions on the potential F at zero or at infinity, we show the existence of infinitely many, radially symmetric solutions of (DI). No symmetry requirement on F is needed. Our approach is based on a non-smooth Ricceri-type variational principle, developed by Marano and Motreanu (J. Differential Equations 182 (2002) 108–120).