Positive solutions to a type of nonlinear three-point boundary value problem with sign changing nonlinearities
In this paper, by using Krasnoselskii's Fixed Point Theorem in a cone, we study the existence of positive solutions for the second-order three-point boundary value problem u ''(t) + a(t)u'(t) + lambda f(t, u(t)) =0, 0 < t < 1, u'(0) = 0, u(1) = alpha u(eta), where 0 < alpha, eta < 1 and f is allowed to change sign. We also give some examples to illustrate our results. (C) 2008 Elsevier Ltd. All rights reserved.
positive solutions three-point boundary value problem krasnoselskii's fixed point theorem cone banach space