Positive solutions for boundary value problem of fractional differential equation with p-Laplacian operator
College of Mathematics and Statistics, Hubei Normal University, Hubei 435002, P.R. China
Boundary Value Problems 2012, 2012:18 doi:10.1186/1687-2770-2012-18Published: 15 February 2012
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
where and 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.