A Liouville comparison principle for solutions of quasilinear differential inequalities

2009/03/10 by Vasilii V. Kurta, Kurta, Vasilii V.
Computer Science · Mathematics · #35J60 #35R45 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.0903.1811

openalex publication_date 2009/03/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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-1u ≤ A(v) + |v|^q-1v on \Bbb Rⁿ, where n≥ 1, q is positive, and the operator A(w) belongs to a class of the so-called α-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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