TITLE:
Existence and Multiplicity of Solutions for Quasilinear p(x)-Laplacian Equations in RN
AUTHORS:
Honghong Qi, Gao Jia
KEYWORDS:
p(x)-Laplacian Operator, Generalized Lebesgue-Sobolev Spaces, Variational Method, Multiple Solutions
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.10,
October
28,
2015
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.