A strong comparison principle for the $p$-Laplacian
Paolo Roselli, Berardino Sciunzi · Proceedings of the American Mathematical Society · 2007
We consider weak solutions of the differential inequality of p-Laplacian type \[ - \Delta _p u - f(u) \le - \Delta _p v - f(v)\] such that $u\leq v$ on a smooth bounded domain in $\mathbb {R}^N$ and either $u$ or $v$ is a weak solution of the corresponding Dirichlet problem with zero boundary condition. Assuming that $u p-1$.