On the Fountain Theorem for Continuous Functionals and Its Application to a Semilinear Elliptic Problem in $\mathbb{R}^2$

Ablanvi Songo; Fabrice Colin

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arXiv · 2509.16059

On the Fountain Theorem for Continuous Functionals and Its Application to a Semilinear Elliptic Problem in $\mathbb{R}^2$

Ablanvi Songo·Fabrice Colin

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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.

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Ablanvi Songo, Fabrice Colin. 2025-09-19. On the Fountain Theorem for Continuous Functionals and Its Application to a Semilinear Elliptic Problem in $\mathbb{R}^2$. https://arxiv.org/abs/2509.16059

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