A boundary value problem for fractional differential equation with p-Laplacian operator at resonance

Abstract

In this paper, by using the coincidence degree theory, we consider the following boundary value problem for fractional p-Laplacian equation D0 +β φp(D0 +αx(t))=f(t,x(t),D0 +αx(t)),t∈[0,1],D0 +αx(0)=D0 +αx(1)=0, where 0 1, φp(s)=| s|p-2s is a p-Laplacian operator. A new result on the existence of solutions for the above fractional boundary value problem is obtained, which generalize and enrich some known results to some extent from the literature. © 2011 Elsevier Ltd. All rights reserved.