On the Fountain Theorem for Continuous Functionals and Its Application to a Semilinear Elliptic Problem in $\mathbb{R}^2$
Analysis of PDEs
2026-04-23 v2
Abstract
In this work, we establish a continuous version of the Fountain theorem by using the framework of the weak slope for continuous functionals, which generalizes Theorem 3.6 of Willem \cite{Wi}. Then we present an application to a semilinear problem.
Cite
@article{arxiv.2509.16059,
title = {On the Fountain Theorem for Continuous Functionals and Its Application to a Semilinear Elliptic Problem in $\mathbb{R}^2$},
author = {Ablanvi Songo and Fabrice Colin},
journal= {arXiv preprint arXiv:2509.16059},
year = {2026}
}