Existence results of three-point boundary value problems for second-order ordinary differential equations

Abstract

We establish existence results of the following three-point boundary value problems: u″ (t) + f (t, u (t)) = 0, t ∈(0, 1), (B C) u (0) = 0 and u (1) = δ u (η), where 0 <η < 1 and 0 < δ ≤ 1. The approach applied in this paper is upper and lower solution method associated with basic degree theory or Schauder`s fixed point theorem. We deal with this problem with the function f which is Carathéodory or singular on its domain. Copyright © 2011 Sheng-Ping Wang and Long-Yi Tsai.