On a functional satisfying a weak Palais-Smale condition

TL;DR

This paper investigates a quasilinear elliptic problem with a functional that meets a weakened Palais-Smale condition, establishing existence results under broad nonlinear assumptions.

Contribution

It introduces a new approach to analyze elliptic problems with weak Palais-Smale conditions, expanding the class of nonlinearities for which solutions can be proven.

Findings

Existence of solutions under general nonlinear assumptions

Extension of Palais-Smale condition to a weaker form

Broader applicability to quasilinear elliptic problems

Abstract

In this paper we study a quasilinear elliptic problem whose functional satisfies a weak version of the well known Palais-Smale condition. An existence result is proved under general assumptions on the nonlinearities.