Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation with p-Laplacian Operator

摘要

In this paper, we deal with the following p-Laplacian fractional boundary value problem: φ_p(D_0~α + u(t)) + f(t,u(t)) =0, 0 ＜ t ＜ 1, u(0) = u'(0) = u'(1) = 0, where 2 ＜ α ≤ 3 is a real number. D_0~α + is the standard Riemann-Liouville differentiation, and f : [0,1] × [0, + ∞) → [0, +∞) is continuous. By the properties of the Green function and some fixed-point theorems on cone, some existence and multiplicity results of positive solutions are obtained. As applications, examples are presented to illustrate the main results.