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

摘要

The upper and lower solutions method is used to study thep-Laplacian fractional boundary value problemD0+γ(ϕp(D0+αu(t)))=f(t,u(t)),0<t<1,u(0)=0,u(1)=au(ξ),D0+αu(0)=0, andD0+αu(1)=bD0+αu(η), where1<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 nonlinearityfcan be singular att=0,1oru=0.