Author(s)

Honghong Qi, Gao Jia

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

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.

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

Qi, H. and Jia, G. (2015) Existence and Multiplicity of Solutions for Quasilinear p(x)-Laplacian Equations in R^N. Journal of Applied Mathematics and Physics, 3, 1270-1281. doi: 10.4236/jamp.2015.310156.