Abstract :
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.
Keywords :
Three-point boundary value problem , Fixed point theorem in a cone , Green’s function , Positive solution
