Positive solutions for a class of higher order boundary value problems with fractional q-derivatives

The authors study the boundary value problem with fractional q-derivatives - (D(q)(v)u)(t) = f(t, u), t is an element of (0, 1), (D(q)(f)u) = 0, i = 0,...,n - 2, (D(q)u)(1) = Sigma(m)(j=1)a(j)(D(q)u)(t(j)) + lambda, where q is an element of (0, 1), m >= 1 and n >= 2 are integers, n - 1 < v <= n, lambda >= 0 f : [0, 1] x R -> [0,infinity) is a parameter, a(i) >= 0 and t(i) is an element of (0, 1) for i = 1,..., m, and D-q(v) is the q-derivative of Riemann-Liouville type of order m. The uniqueness, existence, and nonexistence of positive solutions are investigated in terms of different ranges of lambda. (C) 2012 Elsevier Inc. All rights reserved.