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

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