A Berestycki-Lions type result and applications

TL;DR

This paper presents an abstract theorem ensuring the existence of critical points for functionals, enabling solutions for a broad class of Berestycki-Lions type problems using a deformation lemma on a specialized Pohozaev set.

Contribution

It introduces a new abstract framework and a Pohozaev set approach to establish critical points for functionals related to Berestycki-Lions problems.

Findings

Established an abstract critical point theorem.

Proved solutions exist for a wide class of nonlinear problems.

Applied deformation lemma on a novel Pohozaev set.

Abstract

In this paper we show an abstract theorem involving the existence of critical points for a functional $I$, which permit us to prove the existence of solutions for a large class of Berestycki-Lions type problems. In the proof of the abstract result we apply the deformation lemma on a special set associated with $I$, which we call of Pohozaev set.