An alternative theorem for gradient systems

2020/02/04 by Ricceri, Biagio
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.01413

Abstract

In this paper, given two Banach spaces X, Y and a C¹ functional Φ:X× Y→ \bf R, under general assumptions, we show that either Φ has a saddle-point in X× Y or, for each convex and dense set S⊆ Y, there is some y∈ S such that Φ(⋅, 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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