Infinitely many solutions for elliptic equations with non-symmetric nonlinearities

TL;DR

This paper proves the existence of infinitely many solutions for certain elliptic equations with non-symmetric nonlinearities, introducing a new approach that avoids symmetry deformation techniques.

Contribution

It presents a novel method for establishing multiple solutions in non-symmetric elliptic problems, extending previous techniques and addressing a conjecture by Bahri and Lions.

Findings

Proves existence of infinitely many solutions.

Introduces a new approach applicable to non-symmetric problems.

Avoids deformation from symmetry techniques.

Abstract

We deal with the existence of infinitely many solutions for a class of elliptic problems with non-symmetric nonlinearities. Our result, which is motivated by a well known conjecture formulated by A. Bahri and P.L. Lions, suggests a new approach to tackle these problems. The proof is based on a method which does not require to use techniques of deformation from the symmetry and may be applied to more general non-symmetric problems.