Electron. J. Diff. Eqns., Vol. 2004(2004), No. 142, pp. 1-9.

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

Yulian An, Ruyun Ma

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 less than $b$ less than $\infty$, $a\in C^1[0,\infty)$ 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.

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Yulian An
School of Mathematics, Physics & Software Engineering
Lanzhou Transportation University
Lanzhou 730070, China
email: yulian_an@tom.com
Ruyun Ma
Department of Mathematics
Northwest Normal University
Lanzhou 730070, Gansu, China
email: mary@nwnu.edu.cn

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