Sign-changing solution for an overdetermined elliptic problem on unbounded domain

Guowei Dai, Yong Zhang

We prove the existence of two smooth families of unbounded domains in ${\mathbb{R}}^{N+1}$ with $N\ge 1$ such that \begin{equation} -Δu=λu\,\, \text{in}\,\,Ω, \,\, u=0,\,\,\partia…