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

By Guoqing Chai. Boundary Value Problems, 2012

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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 D0+βφpD0+αu(t)+f(t,u(t))=0,0<t<1,u(0)=0,u(1)+σD0+γu(1)=0,D0+αu(0)=0, where D0+β,D0+α and D0+γ 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.

Subfields: Applied Mathematics, Modeling and Simulation

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