Existence and Multiplicity of Solutions for Quasilinear p(x)-Laplacian Equations in R^N

Honghong Qi, Gao Jia

College of Science, University of Shanghai for Science and Technology, Shanghai, China.

DOI: 10.4236/jamp.2015.310156                

Abstract

We establish some results on the existence of multiple nontrivial solutions for a class of p(x)-Lap-lacian elliptic equations without assumptions that the domain is bounded. The main tools used in the proof are the variable exponent theory of generalized Lebesgue-Sobolev spaces, variational methods and a variant of the Mountain Pass Lemma.

Keywords

p(x)-Laplacian Operator, Generalized Lebesgue-Sobolev Spaces, Variational Method, Multiple Solutions

Conflicts of Interest

The authors declare no conflicts of interest.

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