Multiple critical points theorems for a class of nonsmooth functionals and applications to problems driven by 1-Laplacian and discontinuous nonlinearities

Abstract

In this paper, we present a novel approach to investigate the existence of multiple critical points for a class of nonsmooth functionals. This method provides a robust framework to analyze the existence of solutions for problems involving the $1$-Laplacian operator with discontinuous nonlinearities. Our results contribute to advancing the study of nonsmooth variational problems, by establishing new nonsmooth multiple critical point theorems.