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

Claudianor O. Alves, José L. P. Barreiroy, José Valdo Gonçalves

DOI: http://dx.doi.org/10.12775/TMNA.2016.015

Abstract


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.

Keywords


Variational methods; quasilinear problems; weak solutions

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