A new infinite-dimensional Linking theorem with application to a system of coupled Poisson equations

Ablanvi Songo; Fabrice Colin

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arXiv · 2506.17563

A new infinite-dimensional Linking theorem with application to a system of coupled Poisson equations

Ablanvi Songo·Fabrice Colin

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Abstract

Using the minimax technique from the critical point theory, which consists in constructing or transforming a suitable class of applications such that a critical value $c$ of a functional $f$ can be characterized as a minimax value over this class, we establish a new natural infinite-dimensional linking theorem for strongly indefinite functionals by using the $\tau-$topology of Kryszewski and Szulkin. Our result is a generalization of the classical linking theorem \cite[Theorem 2.21]{Wi}. As an application, we obtain the existence of a nontrivial solution to a system of coupled Poisson equations.

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Ablanvi Songo, Fabrice Colin. 2025-06-21. A new infinite-dimensional Linking theorem with application to a system of coupled Poisson equations. https://arxiv.org/abs/2506.17563

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