Existence of solutions for a class of $p(x)$-Laplacian equations involving a concave-convex nonlinearity with critical growth in $\mathbb{R}^{N}$

Claudianor Oliveira Alves, Marcelo C. Ferreira

DOI: http://dx.doi.org/10.12775/TMNA.2015.020

Abstract


We prove the existence of solutions for a class of quasilinear problems involving variable exponents and with nonlinearity having critical growth. The main tool used is the variational method, more precisely, Ekeland's Variational Principle and the Mountain Pass Theorem.

Keywords


Variational Methods; $p(x)$-Laplacian; critical growth

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