Nonsymmetric sign-changing solutions for the partially overdetermined eigenvalue problem on a hollow cylinder

Guowei Dai, Yingxin Sun, Yong Zhang

Fix $R\in (0,1)$ and $N\ge 2$, and let ${\lambda }_k$ be the $k$th eigenvalue of the radial Dirichlet problem on the annulus $A_R:=\{x\in {\mathbb{R}}^N:R<|x|<1\}$. For every $k\ge 1$ we constru…