Open Access Research

A result on three solutions theorem and its application to p-Laplacian systems with singular weights

Eun Kyoung Lee1 and Yong-Hoon Lee2*

Author Affiliations

1 Department of Mathematics Education, Pusan National University, Busan, 609-735, Korea

2 Department of Mathematics, Pusan National University, Busan, 609-735, Korea

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Boundary Value Problems 2012, 2012:63  doi:10.1186/1687-2770-2012-63

Published: 22 June 2012

Abstract

In this paper, we consider p-Laplacian systems with singular weights. Exploiting Amann type three solutions theorem for a singular system, we prove the existence, nonexistence, and multiplicity of positive solutions when nonlinear terms have a combined sublinear effect at ∞.

MSC: 35J55, 34B18.

Keywords:
p-Laplacian system; singular weight; upper solution; lower solution; three solutions theorem