Uniqueness of positive radial solutions of a semilinear elliptic equation in an annulus
Uniqueness of positive radial solutions of a semilinear elliptic equation in an annulus
In this paper, we show the following equation \begin{document}$\begin{cases} Δ u+u^{p}+λ u = 0&\text{ in }Ω,\\ u = 0&\text{ on }\partialΩ, \end{cases}$ \end{document} has at most one positive radial solution for a certain range of $λ>0$. Here $p>1$ and $Ω$ is the annulus $\{x∈{{\mathbb{R}}^{n}}:a<|x|<b\}$, $0<a<b$. We also show this solution …