An infinite-dimensional mountain pass theorem with applications to nonlinear elliptic systems

Ablanvi Songo; Fabrice Colin

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arXiv · 2512.02229

An infinite-dimensional mountain pass theorem with applications to nonlinear elliptic systems

Ablanvi Songo·Fabrice Colin

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Abstract

The purpose of this paper is to establish a critical point theorem, which is an infinite-dimensional generalization of the classical generalized Mountain Pass Theorem of P. H. Rabinowitz \cite[Theorem 5.3]{Ra}. As application, we obtain the existence of at least one solution to a semilinear elliptic systems with indefinite weights in $\mathbb{R}^2$.

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Ablanvi Songo, Fabrice Colin. 2025-12-01. An infinite-dimensional mountain pass theorem with applications to nonlinear elliptic systems. https://arxiv.org/abs/2512.02229

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