Multiple solutions for a class of quasilinear problems involving variable exponents

TL;DR

This paper establishes the existence of multiple solutions for a class of quasilinear problems with variable exponents in Euclidean space using variational methods and Nehari manifold properties.

Contribution

It introduces new multiplicity results for quasilinear problems involving variable exponents using direct variational techniques.

Findings

Proves the existence of multiple solutions.

Utilizes Ekeland's variational principle.

Employs properties of the Nehari manifold.

Abstract

In this paper we prove the multiplicity of solutions for a class of quasilinear problems in $ \mathbb{R}^{N} $ involving variable exponents. The main tool used is in the proof are the direct methods, Ekeland's variational principle and some properties related to Nehari manifold.