Positive solutions of a nonlinear four-point boundary value problems in Banach spaces

In this paper, by using the fixed points of strict-set-contractions, we study the existence of at least one or two positive solutions to the four-point boundary value problem y ''(t) + a (t) f(y(t)) = theta, 0 < t < 1, y(0) = mu y(xi), y(1) = beta y(eta), in Banach space E, where theta is zero element of E, 0 < xi <= eta < 1, 0 < mu < (1)/(1-xi), 0 < beta < (1)/(eta) and mu xi(1-beta) + (1-mu)(1-beta eta) > 0. As an application, we also give one example to demonstrate our results. (c) 2004 Elsevier Inc. All rights reserved.