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

Ismael Sandro da Silva; Marcos T. O. Pimenta; Pedro Fellype Pontes

doi:10.48550/arxiv.2602.20858

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

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Ismael Sandro da Silva, Marcos T. O. Pimenta, Pedro Fellype Pontes

DOI: 10.48550/arxiv.2602.20858

Cited by: 0

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.

Fields of Study & Subjects

Nonlinear Partial Differential Equations Optimization and Variational Analysis Nonlinear Differential Equations Analysis

Publication details

Journal / source: arXiv (Cornell University)
Publication date: 24 February 2026
Language: EN
Document type: Preprint