Hopf maximum principle violation for elliptic equations with non-Lipschitz nonlinearity

Yavdat Il'yasov, Youri Egorov

We consider elliptic equations with non-Lipschitz nonlinearity $$-\Delta u=\lambda |u{|}^{\beta -1}u-|u{|}^{\alpha -1}u$$ in a smooth bounded domain $\Omega \subset {\mathbb{R}}^n$, $n\ge 3$, with Dirichlet bound…