The positive properties of green's function for fractional differential equations and its applications

Abstract

We consider the properties of Green's function for the nonlinear fractional differential equation boundary value problem: D0+αu (t) + f (t, u (t)) + e (t) = 0, 0 < t < 1, u (0) = u ' (0) = = u (n - 2) (0) = 0, u (1) = β u (η), where n - 1 < α ≤ n, n ≥ 3,0 < β ≤ 1,0 ≤ η ≤ 1, D0+α is the standard Riemann-Liouville derivative. Here our nonlinearity f may be singular at u = 0. As applications of Green's function, we give some multiple positive solutions for singular boundary value problems by means of Schauder fixed-point theorem. © 2013 Fuquan Jiang et al.