Entire solutions of the inequality div\((A| Du|)Du\geqq f(u)\)
type: Item
instance of: scholarly article
title: Entire solutions of the inequality div\((A| Du|)Du\geqq f(u)\)
zbMATH Open document ID: 0869.35117
DOI: 10.1007/PL00004596
author: Yūki Naito
author: Hiroyuki Usami
published in: Mathematische Zeitschrift
publication date: 1997-07-03T00:00:00Z
review text: This paper is concerned with quasilinear elliptic inequalities of the form \[ \text{div}(A(|Du|)Du)\geq f(u),\quad x\in\mathbb{R}^N, \] where \(f\not\equiv 0\) is a nonnegative continuous function on \([0,\infty)\) vanishing only at zero. Typical functions \(A\) we are interested in, are \[ A(p)= p^{m-2},\quad m>1,\quad A(p)= (1+p^2)^{-\alpha},\quad \alpha\leq 1/2, \] and so on. We obtain existence and nonexistence criteria of nonnegative nontrivial entire solutions of the inequality.
Mathematics Subject Classification ID: 35R45
Mathematics Subject Classification ID: 35J85
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 1028183
zbMATH Keywords: quasilinear elliptic inequalities
zbMATH Keywords: existence
zbMATH Keywords: nonexistence
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1028183