Uniqueness of positive solutions of a class of ODE with nonlinear boundary conditions. (13th November 2005)

• Record Type: Journal Article
• Authors: Ma, Ruyun; An, Yulian
• Is Part Of: Boundary value problems. Volume 3(2005)
• Page Start: 289
• Page End: 298
• Publication Date: 2005-11-13
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/BVP.2005.289
• Languages: English
• ISSNs: 1687-2762

Abstract

Abstract : We study the uniqueness of positive solutions of the boundary value problemu ″ + a ( t ) u ′ + f ( u ) = 0, t ∈ ( 0, b ), B 1 ( u ( 0 ) ) − u ′ ( 0 ) = 0, B 2 ( u ( b ) ) + u ′ ( b ) = 0, where0 < b < ∞, B 1 andB 2 ∈ C 1 ( ℝ ), a ∈ C [ 0, ∞ ) witha ≤ 0 on[ 0, ∞ ) andf ∈ C [ 0, ∞ ) ∩ C 1 ( 0, ∞ ) satisfy suitable conditions. The proof of our main result is based upon the shooting method and the Sturm comparison theorem.