# A global minimization trick to solve some classes of Berestycki-Lions type problems

## TL;DR

This paper introduces an abstract theorem that guarantees solutions for certain elliptic equations, including zero mass problems, and demonstrates the existence of multiple solutions, advancing understanding in this mathematical area.

## Contribution

The paper presents a novel abstract theorem applicable to Berestycki-Lions type problems, establishing solution existence and multiplicity for zero mass elliptic equations.

## Key findings

- Proved an abstract theorem for elliptic equations.
- Established multiple solutions for zero mass problems.
- Extended solution existence results to new problem classes.

## Abstract

In this paper we show an abstract theorem that can be used to prove the existence of solution for a class of elliptic equation considered in Berestycki-Lions \cite{berest} and related problems. Moreover, we use the abstract theorem to show that a class of zero mass problems has multiple solutions, which is new for this type of problem.