Infinitely Many Critical Points of Non-Differentiable Functions and Applications to a Neumann-Type Problem Involving the p-Laplacian

Abstract

For a family of functionals in a Banach space, which are possibly non-smooth and depend also on a positive real parameter, the existence of a sequence of critical points (according to Motreanu and Panagiotopoulos (“Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities,” Nonconvex Optimization Applications, Vol. 29, Kluwer, Dordrecht, 1998, Chap. 3)) is established by mainly adapting a new technique due to Ricceri (2000, J. Comput. Appl. Math.113, 401–410). Two applications are then presented. Both of them treat the Neumann problem for an elliptic variational–hemivariational inequality with p-Laplacian.