New minimax theorems for lower semicontinuous functions and applications
Analysis of PDEs
2023-06-16 v1
Abstract
In this paper we prove a version of the Fountain Theorem for a class of nonsmooth functionals that are sum of a functional and a convex lower semicontinuous functional, and also a version of a theorem due to Heinz for this class of functionals. The new abstract theorems will be used to prove the existence of infinitely many solutions for some elliptic problems whose the associated energy functional is of the above mentioned type. We study problems with logarithmic nonlinearity and a problem involving the 1-Laplacian operator.
Cite
@article{arxiv.2306.09051,
title = {New minimax theorems for lower semicontinuous functions and applications},
author = {Claudianor O Alves and Giovanni Molica Bisci and Ismael S. da Silva},
journal= {arXiv preprint arXiv:2306.09051},
year = {2023}
}