Multiplicity of solutions of some quasilinear equations in   ${\mathbb{R}^{N}}$ with variable exponents and concave-convex nonlinearities
  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. 
Claudianor O. Alves, Jos\'e L. P. Barreiro and Jos\'e V. A.   Gon\c{c}alves
math.AP