On the uniqueness of solutions of a semilinear equation in an annulus

Carmen Cortázar; Marta Garcia-Huidobro; Pilar Herreros; Satoshi Tanaka

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arXiv · 2009.04580

On the uniqueness of solutions of a semilinear equation in an annulus

Carmen Cortázar·Marta Garcia-Huidobro·Pilar Herreros·Satoshi Tanaka

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Abstract

We establish the uniqueness of positive radial solutions of $$\begin{cases} Δu +f(u)=0,\quad x\in A \\ u(x) =0 \quad x\in \partial A \end{cases} $$ where $A:=A_{a,b}=\{ x\in {\mathbb R}^n : a<|x| 0$ for all $s>0$, or has one zero at $B>0$, is non positive and not identically 0 in $(0,B)$ and it is positive in $(B,\infty)$.

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Carmen Cortázar, Marta Garcia-Huidobro, Pilar Herreros, Satoshi Tanaka. 2020-09-09. On the uniqueness of solutions of a semilinear equation in an annulus. https://arxiv.org/abs/2009.04580

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