Solvability for a class of fractional m-point boundary value problem at resonance

In this paper, the following fractional ordinary differential equation boundary value problem: D(0+)(alpha)u(t) = f(t, u(t), D(0+)(alpha-1)u(t)) + e(t), 0 < t < 1, I(0+)(2-alpha)u(t)vertical bar(t=0) =0, u(1) = Sigma(m-2)(i=1)beta(i)u(eta(i)), is considered, where 1 < alpha <= 2 is a real number, D-0+(alpha) and I-0+(alpha) are the standard Riemann-Liouville differentiation and integration, and f : [0, 1] x R-2 -> R is continuous and e is an element of L-1[0, 1], and beta(i) is an element of R, i = 1, 2, ... , m - 2, 0 < eta(1) <eta(2) < ... < eta(m-2) < 1 are given constants such that Sigma(M-2)(i=1) beta(i)eta(alpha-1)(i) = 1. By using the coincidence degree theory, some existence results of solutions can be established. (C) 2011 Elsevier Ltd. All rights reserved.