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) = θ, 0 < t <1, y(0) = μy(ξ ), y(1) = βy(η), in Banach space E, where θ is zero element of E, 0 < ξ η < 1, 0<μ< 1 1−ξ , 0 < β < 1 η and μξ(1 − β) + (1 − μ)(1 − βη) > 0. As an application, we also give one example to demonstrate our results.  2004 Elsevier Inc. All rights reserved