Three positive solutions of a nonlinear three-point boundary value problem

In this paper, existence criteria for three positive solutions of the nonlinear three-point boundary value problem u (t )+ a(t)u (t )+ b(t)u(t)+ h(t)f (u) = 0, t∈ (0, 1), u(0) = 0, u(1) = αu(η), are established by using the Leggett–Williams fixed point theorem. An example is also included to illustrate the importance of the result obtained.  2003 Elsevier Inc. All rights reserved