Multiple solutions for a class of quasilinear problems involving   variable exponents
  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. 
Claudianor O. Alves and Jos\'e L. P. Barreiro
math.AP