Positive solutions for eigenvalue problems of fractional differential equation with p-Laplacian

Abstract

In this paper, we investigate the existence of positive solutions for the eigenvalue problem of nonlinear fractional differential equation with p-Laplacian operator D 0+( p(D 0+u(t))) = f(u(t)), 0 1, −1 p = q, 1/p + 1/q = 1, > 0 is a parameter, and f : (0,+1) ! (0,+1) is continuous. By using the properties of the Green function and the Guo–Krasnosel’skii fixed-point theorem on cones, several new existence results of at least one or two positive solutions in terms of different eigenvalue interval are obtained. Moreover, the nonexistence of positive solution in term of the parameter is also considered.