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.