Eigenvalue of Fractional Differential Equations with p-Laplacian Operator

Abstract EN

We investigate the existence of positive solutions for the fractional order eigenvalue problem with p-Laplacian operator -?tβ(φp(?tαx))(t)=λf(t,x(t)), t∈(0,1), x(0)=0, ?tαx(0)=0, ?tγx(1)=∑j=1m-2aj?tγx(ξj), where ?tβ, ?tα, ?tγ are the standard Riemann-Liouville derivatives and p-Laplacian operator is defined as φp(s)=|s|p-2s, p>1.f:(0,1)×(0,+∞)→[0,+∞) is continuous and f can be singular at t=0,1 and x=0.

By constructing upper and lower solutions, the existence of positive solutions for the eigenvalue problem of fractional differential equation is established.