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

TL;DR

This paper develops new nonsmooth multiple critical point theorems to analyze solutions of problems involving the 1-Laplacian operator with discontinuous nonlinearities, advancing the understanding of nonsmooth variational problems.

Contribution

It introduces a novel approach to establish multiple critical points for nonsmooth functionals, specifically applied to 1-Laplacian problems with discontinuous nonlinearities.

Findings

Established new nonsmooth multiple critical point theorems

Proved existence of solutions for 1-Laplacian problems with discontinuities

Enhanced the theoretical framework for nonsmooth variational analysis

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.