Multiplicity results for a three-point boundary value problem at resonance

This paper deals with second-order three-point boundary value problem u"(t) = f(t,u(t)), t is an element of (0,1), u(0) = 0, u(1) = alphau(eta), where f : [0, 1] x R --> R is continuous, alpha is an element of (0, infinity) and eta is an element of (0, 1) are given constants such that alphaeta = 1. We develop the methods of lower and upper solutions by the connectivity properties of the solution set of parameterized families of compact vector fields. As applications of these methods, we get several multiplicity results for the problems under consideration. (C) 2003 Elsevier Science Ltd. All rights reserved.