An alternative theorem for gradient systems

Biagio Ricceri

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arXiv · 2002.01413

An alternative theorem for gradient systems

Biagio Ricceri

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Abstract

In this paper, given two Banach spaces $X, Y$ and a $C^1$ functional $\Phi:X\times Y\to {\bf R}$, under general assumptions, we show that either $\Phi$ has a saddle-point in $X\times Y$ or, for each convex and dense set $S\subseteq Y$, there is some $\tilde y\in S$ such that $\Phi(\cdot,\tilde y)$ has at least three critical points in $X$, two of which are global minima. Also, an application to non-cooperative elliptic systems is presented.

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Biagio Ricceri. 2020-02-04. An alternative theorem for gradient systems. https://arxiv.org/abs/2002.01413

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