Uniqueness of positive solutions of a class of ODE with nonlinear boundary conditions. (13th November 2005) - Ma, Ruyun; An, Yulian
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.