Nonnegative solutions of some quasilinear elliptic inequalities and applications

Abstract

Let $f:\mathbb{R}\to \mathbb{R}$ be a continuous function. We prove that under some additional assumptions on $f$ and $A:\mathbb{R}\to {\mathbb{R}}_{+}$, weak $\Cuno$ solutions of the differential inequality $-\diver(A(\abs{\nabla u})\nabla u)\ge f(u)$ on $\RN$ are nonnegative. Some extensions of the result in the framework of subelliptic operators on Carnot Groups are considered.

arXiv comment20 pages

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