| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 10 | |
| Number of page(s) | 43 | |
| DOI | https://doi.org/10.1051/cocv/2024005 | |
| Published online | 10 February 2025 | |
New minimax theorems for lower semicontinuous functions and applications
1
Unidade Acadêmica de Matemática, Universidade Federal de Campina Grande, 58429-970 Campina Grande, PB, Brazil
2
Dipartimento di Scienze Pure e Applicate (DiSPeA), Università degli Studi di Urbino Carlo Bo, Piazza della Repubblica 13, 61029 Urbino (Pesaro e Urbino), Italy
* Corresponding author: ismael.music3@gmail.com
Received:
14
April
2022
Accepted:
13
January
2024
The classical Fountain Theorem is extended to the case of functionals I which are the sum of a C1 term and of a convex lower semicontinuous functional. In this setting a suitable nonsmooth version of a Heinz’s result has been proved in order to obtain a dual version of the main Fountain’s type result. Moreover, as a byproduct of the theoretical arguments presented here, some applications concerning the existence of infinitely many solutions for a wide class of differential problems are also presented. More precisely, elliptic problems involving either a logarithmic nonlinearity or driven by the 1-Laplacian operator have been studied.
Mathematics Subject Classification: 35J15 / 35J20 / 26A27
Key words: Fountain Theorem / semicontinuous functional / logarithmic nonlinearity / 1-Laplacian operator
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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