On bounded positive solutions of quasilinear elliptic equations in \(R^ n\)
type: Item
instance of: scholarly article
title: On bounded positive solutions of quasilinear elliptic equations in \(R^ n\)
zbMATH Open document ID: 0699.35085
author: Nichiro Kawano
published in: Proceedings of the Japan Academy. Series A
publication date: 1988-01-01T00:00:00Z
review text: If \(\phi \in C^ 0([0,\infty))\), \(\phi\geq 0\), \(\not\equiv 0\) and \(\int^{\infty}_{0}r\phi (r) dr<\infty\), then the problems \[ \nabla \cdot (\frac{\nabla u}{\sqrt{1+| \Delta u|^ 2}})=\pm \phi (| x|)u^ q,\quad q>1, \] have infinitely many bounded positive entire solutions \(u\in C^ 2({\mathbb{R}}^ n)\) (n\(\geq 3)\), \(u=u(| x|)\), each of which tends to a positive constant as \(| x| \to \infty\).
reviewed by: G. Dziuk
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 4146558
zbMATH Keywords: minimal surface equation
zbMATH Keywords: quasilinear elliptic equation
zbMATH Keywords: positive entire solutions
MaRDI profile type: Publication
full work available at URL: pjaa.64.187
OpenAlex ID: W2051115778
cites work: On bounded entire solutions of semilinear elliptic equations
cites work: On the positive solutions of an Emden-type elliptic equation
cites work: Q3027502
cites work: Nonexistence theorems for singular solutions of quasilinear partial differential equations
DOI: 10.3792/PJAA.64.187
description: scientific article; zbMATH DE number 4146558