Open Access Research

A note on the existence of solutions for a class of quasilinear elliptic equations: an Orlicz-Sobolev space setting

Yang Yang1* and Jihui Zhang2

Author Affiliations

1 School of Science, Jiangnan University, Wuxi, 214122, People’s Republic of China

2 School of Mathematics Science, Nanjing Normal University, Nanjing, 210097, People’s Republic of China

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Boundary Value Problems 2012, 2012:136  doi:10.1186/1687-2770-2012-136

Published: 22 November 2012

Abstract

In this note, we study the existence and multiplicity of solutions for the quasilinear elliptic problem as follows:

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/136/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/136/mathml/M1">View MathML</a>

where <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/136/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/136/mathml/M2">View MathML</a> is a bounded domain with a smooth boundary. The existence and multiplicity of solutions are obtained by a version of the symmetric mountain pass theorem.

Keywords:
Orlicz-Sobolev spaces; symmetric mountain pass theorem; quasilinear elliptic equations