Hopf maximum principle violation for elliptic equations with non-Lipschitz nonlinearity
Yavdat Shavkatovich Il'yasov, Youri V. Egorov · arXiv (Cornell University) · 2009
We consider elliptic equations with non-Lipschitz nonlinearity $$ -Δu = λ|u|^{β-1}u-|u|^{α-1}u$$ in a smooth bounded domain $Ω\subset \mathbb{R}^n$, $n\geq 3$, with Dirichlet boundary conditions; here $02(1+α) (1+β)/(1-α)(1-β)$.