Multiple positive solutions for second-order m-point boundary value problems ✩

In this paper, the second-order m-point boundary value problem u (t) + f (t,u) = 0, 0 t 1, u(0) = 0, u (1) − m−2 i=1 kiu (ξi ) = 0 is studied, where ki > 0 (i = 1, 2, . . . , m−2), 0 < ξ1 < ξ2 < ··· < ξm−2 < 1.We give at first the associated Green’s function and its properties for the m-point boundary value problem, and growth conditions are imposed on f which yield the existence of at least three positive solutions by using the five functionals fixed point theorem and the properties. © 2006 Elsevier Inc. All rights reserved.