Two positive Fisher--KPP equilibria on a uniformly smooth unbounded domain

We construct a connected unbounded domain in $\R^{21}$ with uniformly $C^{2,1/2}$ boundary on which the Dirichlet Fisher--KPP equation has two distinct bounded positive equilibria. The boundary consists of two smooth global graphs whose separation tends to the critical slab width. A corrected transverse mode gives a slowly decaying subsolution, while a compact enlargement of the domain permits a second equilibrium with a faster upper bound. The example gives a negative answer to the unrestricted strong-KPP uniqueness question. No optimal dimension is asserted.