Some remarks on the supersolution-subsolution method for superlinear elliptic equations
type: Item
instance of: scholarly article
title: Some remarks on the supersolution-subsolution method for superlinear elliptic equations
zbMATH Open document ID: 0632.35022
DOI: 10.1016/0022-247X(87)90298-8
author: Nobuyoshi Fukagai
author: Kiyoshi Yoshida
author: Takaši Kusano
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: The authors study the equation \(\Delta u+K(x)u^ p=0\), where \(x\in {\mathbb{R}}^ n\), \(n\geq 3\), \(p>1\), and K is positive. They show that it is in general impossible to prove the existence of a non-trivial solution to this equation by an effective construction of sub- and supersolutions since if v and w, \(0\leq v\leq w\), are sub- and supersolution, respectively, then, under suitable decay hypothesis on K and W it follows already that \(v=w\) is a solution. This theorem is based on a second result in the paper which says that under corresponding hypotheses any nonnegative subsolution is \(O(| x|^{2-n})\) for \(| x| \to \infty\).
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 4027985
zbMATH Keywords: semilinear
zbMATH Keywords: scalar field equations
zbMATH Keywords: existence
zbMATH Keywords: sub- and supersolutions
zbMATH Keywords: nonnegative subsolution
reviewed by: F. Tomi
MaRDI profile type: Publication
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full work available at URL: 0022-247x(87)90298-8
OpenAlex ID: W2064774533
description: scientific article; zbMATH DE number 4027985