Multiple Positive Solutions for a Nonlinear Three-Point Integral Boundary-Value Problem

Abstract

We investigate the existence of positive solutions to the nonlinear second-order three-point integral boundary value problem. u′′(t) + f(t, u(t)) = 0, 0 < t < T, u(0) = βu(η), u(T ) = α ∫ η 0 u(s)ds, where 0 < η < T , 0 < α < 2T η2 , 0 < β < 2T−αη 2 αη2−2η+2T are given constants. We establish the existence of at least three positive solutions by using the Leggett-Williams fixed-point theorem.