English

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.

Keywords

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}
}