IJPAM: Volume 12, No. 1 (2004)

UNIQUENESS OF POSITIVE RADIAL SOLUTIONS
FOR $\triangle{u}+f(u)=0$ ON THE ANNULUS

Samuel Jator$^1$, Zachariah Sinkala$^2$
$^1$Department of Mathematics
AustinPeay State University
Clarksville, TN 37044, USA
e-mail: JatorS@apsu.edu
$^2$Department of Mathematical Sciences
Middle Tennessee State University
Murfreesboro, TN 37132, USA
e-mail: zsinkala@mtsu.edu


Abstract.In this paper we prove uniqueness of positive solutions to the semilinear equation $\triangle{u}+f(u)=0$ subject to the Dirichlet boundary condition on an annulus in $\Re^{n},n\geq 3$. The result applies to a wide class of nonlinear functions $f$, for example , nonlinear functions of type $f(u)=\sum_{k=1}^{\nu}a_{k}u^{p_{k}},1=p_{1}<p_{2}<...<p_{\nu}=p$,

Received: December 19, 2003

AMS Subject Classification: 34B16, 34B16

Key Words and Phrases: Dirichlet boundary conditions, radial solution, shooting method

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 12
Issue: 1