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Open Access Research

Multiple solutions for a p-Laplacian elliptic problem

Jing Zeng1 and Shuting Cai2*

Author Affiliations

1 School of Mathematics and Computer Sciences, Fujian Normal University, Fuzhou, 350007, P.R. China

2 Department of Mathematics and Physics, Fujian Jiangxia University, Fuzhou, 350108, P.R. China

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Boundary Value Problems 2014, 2014:124  doi:10.1186/1687-2770-2014-124

Published: 20 May 2014

Abstract

We consider the following p-Laplacian elliptic equation on <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/124/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/124/mathml/M1">View MathML</a>: <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/124/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/124/mathml/M2">View MathML</a>. For certain <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/124/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/124/mathml/M3">View MathML</a>, we are interested in the functional on a group invariant subspace, and we obtain the existence of infinitely many radial solutions and non-radial solutions of the equation, which extends the result of (Bartsch and Willem in J. Funct. Anal. 117:447-460, 1993) to the space <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/124/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/124/mathml/M4">View MathML</a>.

Keywords:
p-Laplacian; infinitely many radial solutions and non-radial solutions; group invariant