A Liouville comparison principle for solutions of quasilinear differential inequalities

Details A Liouville comparison principle for solutions of quasilinear differential inequalities A Liouville comparison principle for solutions of quasilinear differential inequalities

2009-03-10

arxiv.org/abs/0903.1811v3

Mathematics

Analysis of PDEs

This paper has been withdrawn by the author.

Scientific paper

This work is devoted to the study of a Liouville comparison principle for entire weak solutions of quasilinear differential inequalities of the form $A(u) + |u|^{q-1}u \leq A(v) + |v|^{q-1}v$ on ${\Bbb R}^n$, where $n\geq 1$, $q$ 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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