Existence Results of Three-Point Boundary Value Problems for Second-order Ordinary Differential Equations. (28th September 2010) - Wang, Sheng-Ping; Tsai, Long-Yi
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 andu ( 1 ) = δ u ( η ), where0 < η < 1 and0 < 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 functionf which is Carathéodory or singular on its domain.