Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 142, pp. 1-9.

Title: Uniqueness of positive solutions for a class of ODE's
       with Dirichlet boundary conditions

Authors: Yulian An (Lanzhou Transportation Univ., China)
         Ruyun Ma (Northwest Normal Univ., Lanzhou, China)

Abstract: 
 We study the uniqueness of positive solutions of the boundary-value
 problem
 $\displaylines{
 u''+a(t)u'+f(t,u)=0 ,\quad t\in (0,b)\cr
 u(0)=0,u(b)=0\,,
 }$$
 where $0<b<\infty$, $a\in C^1[0,\infty)$ and
 $f\in C^1([0,\infty)\times [0, \infty), [0, \infty))$ satisfy suitable
 conditions.  The proof of our main result is based on the shooting method
 and the Sturm comparison theorem.

Submitted August 18, 2004. Published November 29, 2004.
Math Subject Classifications: 34B15.
Key Words: Boundary value problem; positive solutions; uniqueness;
           shooting method; Sturm comparison theorem.