Positive solutions for three-point boundary value problems with dependence on the first order derivative ✩

A new fixed point theorem in a cone is applied to obtain the existence of at least one positive solution for the second order three-point boundary value problem x + f (t,x,x ) = 0, 0 < t <1, x(0) = 0, x(1) = αx(η), where f is a nonnegative continuous function, α > 0, η ∈ (0, 1), αη < 1. The associated Green’s function for the above problem is also used.  2003 Elsevier Inc. All rights reserved.