Strong-KPP uniqueness conjecture for positive bounded solutions in general domains

Let $(\Omega,\varrho)$ be a domain with the boundary conditions and elliptic problem specified by

, and let $f$ be a strong-KPP reaction. **Strong-KPP uniqueness conjecture.** In a general domain,

admits at most one positive bounded solution. The paper's methods do not treat critical eigenvalues approaching or equal to $f'(0)$, so uniqueness in this generality remains open.