A Liouville comparison principle for solutions of quasilinear differential inequalities

Abstract

This work is devoted to the study of a Liouville comparison principle for entire weak solutions of quasilinear differential inequalities of the form $A(u)+|u{|}^{q-1}u\le A(v)+|v{|}^{q-1}v$ on ${\mathbb{R}}^n$, where $n\ge 1$, $q$ is positive, and the operator $A(w)$ belongs to a class of the so-called $\alpha$-monotone operators. Typical examples of such operators are the $p$-Laplacian and its well-known modifications. The results improve and supplement those in [1].

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