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

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.