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

In this paper, we investigate the existence of positive solutions for the eigenvalue problem of nonlinear fractional differential equation with p-laplacian operator:d^β_0 + (φ^ α_0 + u(t))) = λf(u(t)), 0 1; <1 p = q; 1=p + 1=q = 1; λ > 0 is a parameter, and f : (0, +∞) → (0,+∞) is continuous. by using the properties of the green function and the guo{krasnosel'skii xed-point theorem on cones, several new existence results of at least one or two positive solutions, in terms of dierent eigenvalue intervals, are obtained. moreover, the nonexistence of positive solution, in terms of parameter λ, is also considered.