Boundary Value Problems
Volume 2005 (2005), Issue 3, Pages 289-298
doi:10.1155/BVP.2005.289

Uniqueness of positive solutions of a class of ODE with nonlinear boundary conditions

Ruyun Ma1 and Yulian An2

1Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
2Physical Software & Engineering, Lanzhou Jiaotong University, Gansu, Lanzhou 730070, China

Received 19 August 2004; Revised 27 January 2005

Copyright © 2005 Ruyun Ma and Yulian An. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the uniqueness of positive solutions of the boundary value problem u″+a(t)u′+f(u)=0, t∈(0,b), B1(u(0))−u′(0)=0, B2(u(b))+u′(b)=0, where 0<b<∞, B1 and B2∈C1(ℝ), a∈C[0,∞) with a≤0 on [0,∞) and f∈C[0,∞)∩C1(0,∞) satisfy suitable conditions. The proof of our main result is based upon the shooting method and the Sturm comparison theorem.