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Open Access Research

Positive solutions for boundary value problem of fractional differential equation with p-Laplacian operator

Guoqing Chai

Author Affiliations

College of Mathematics and Statistics, Hubei Normal University, Hubei 435002, P.R. China

Boundary Value Problems 2012, 2012:18  doi:10.1186/1687-2770-2012-18

Published: 15 February 2012

Abstract

In this article, the author investigates the existence and multiplicity of positive solutions for boundary value problem of fractional differential equation with p-Laplacian operator

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where <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/18/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/18/mathml/M2">View MathML</a> and <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/18/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/18/mathml/M3">View MathML</a> are the standard Riemann-Liouville derivatives with 1 < α ≤ 2, 0 < β ≤ 1, 0 < γ ≤ 1, 0 ≤ α - γ - 1, the constant σ is a positive number and p-Laplacian operator is defined as φp(s) = |s|p-2s, p > 1. By means of the fixed point theorem on cones, some existence and multiplicity results of positive solutions are obtained.

2010 Mathematical Subject Classification: 34A08; 34B18.

Keywords:
fractional differential equations; fixed point index; p-Laplacian operator; positive solution; multiplicity of solutions