## Differential and Integral Equations

### Uniqueness of positive radial solutions of $\Delta u+f(\vert x\vert ,u)=0$

#### Abstract

We study the uniqueness of positive radial solutions to the Dirichlet boundary value problem for the semilinear elliptic equation $\Delta u+f(|x|,u)=0$ in a finite ball or annulus in $R^n$, $n\ge 3$. Applying our main results to the cases when $f$ is independent of $t$, or $f$ is of the form $K(t)u^p$, we can establish some earlier known results and obtain some new results in an easier and unified approach.

#### Article information

Source
Differential Integral Equations, Volume 11, Number 5 (1998), 725-743.

Dates
First available in Project Euclid: 30 April 2013

Erbe, Lynn; Tang, Moxun. Uniqueness of positive radial solutions of $\Delta u+f(\vert x\vert ,u)=0$. Differential Integral Equations 11 (1998), no. 5, 725--743. https://projecteuclid.org/euclid.die/1367329667