Parameter-uniform Robin uniqueness on large dilations

Berestycki and Graham proved large-dilation uniqueness for bounded positive solutions of $-Δu=f(u)$ in $κΩ$, with $u+α\partial_νu=0$ on $\partial(κΩ)$, when $α$ is fixed, and remarked that the dilation threshold should not depend on $α$. We show that it does not, including at the Dirichlet and Neuma