Existence Results of Three-Point Boundary Value Problems for Second-order Ordinary Differential Equations. (28th September 2010)

• Record Type: Journal Article
• Authors: Wang, Sheng-Ping; Tsai, Long-Yi
• Other Names: Franco Daniel Academic Editor.
• Is Part Of: Boundary value problems. Volume 2011(2011)
• Publication Date: 2010-09-28
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2011/901796
• Languages: English
• ISSNs: 1687-2762

Abstract

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.