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Open Access Research

Positive solution for boundary value problems with p-Laplacian in Banach spaces

Dehong Ji1* and Weigao Ge2

Author affiliations

1 College of Science, Tianjin University of Technology, Tianjin 300384, China

2 School of Science, Beijing Institute of Technology, Beijing 100081, China

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Citation and License

Boundary Value Problems 2012, 2012:51  doi:10.1186/1687-2770-2012-51

Published: 30 April 2012

Abstract

In this article, by using the fixed point theorem of strict-set-contractions operator, we discuss the existence of positive solution for boundary value problems with p-Laplacian

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/51/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/51/mathml/M1">View MathML</a>

in Banach spaces E, where: θ is the zero element of E. Although the fixed point theorem of strict-set-contractions operator is used extensively in yielding positive solutions for boundary value problems in Banach spaces, this method has not been used to study those boundary value problems with p-Laplacian in Banach spaces. So this article may be regarded as an illustration of fixed point theorem of strict-set-contractions operator in a new area.

MSC: 34B18.

Keywords:
boundary value problems; p-Laplacian; positive solution; strict-set-contractions