Multiplicity of solutions of some quasilinear equations in ${\mathbb{R}^{N}}$ with variable exponents and concave-convex nonlinearities

TL;DR

This paper demonstrates the existence of multiple solutions for a class of quasilinear equations in Euclidean space involving variable exponents and concave-convex nonlinearities, using advanced variational methods.

Contribution

It introduces new multiplicity results for quasilinear problems with variable exponents and nonlinearities of concave-convex type, employing Ekeland's principle and Nehari manifolds.

Findings

Proved the existence of multiple solutions for the class of equations.

Applied variational methods effectively to problems with variable exponents.

Extended known results to more general quasilinear equations in bR^N.

Abstract

In this paper, we prove multiplicity of solutions for a class of quasilinear problems in $ \mathbb{R}^{N} $ involving variable exponents and nonlinearities of concave-convex type. The main tools used are variational methods, more precisely, Ekeland's variational principle and Nehari manifolds.