Upper and Lower Solutions Method for a Class of Singular Fractional Boundary Value Problems with p-Laplacian Operator

Abstract

The upper and lower solutions method is used to study the p-Laplacian fractional boundary value problem D0+γ(ϕp(D0+αu(t)))=f(t,u(t)), 0<t<1, u(0)=0, u(1)=au(ξ), D0+αu(0)=0, and D0+αu(1)=bD0+αu(η), where 1<α,γ⩽2,0⩽a,b⩽1,0<ξ,η<1. Some new results on the existence of at least one positive solution are obtained. It is valuable to point out that the nonlinearity f can be singular at t=0,1 or u=0.