Asymptotic results for finite energy solutions of semilinear elliptic equations
type: Item
instance of: scholarly article
title: Asymptotic results for finite energy solutions of semilinear elliptic equations
zbMATH Open document ID: 0778.35009
DOI: 10.1016/0022-0396(92)90103-T
author: Henrik Egnell
published in: Journal of Differential Equations
publication date: 1992-08-13T00:00:00Z
review text: The author studies nonnegative (weak) solutions \(u:\mathbb{R}^ n\to\mathbb{R}\), \(n\geq 3\), of differential inequalities of the principal form \(\Delta u+f(x,u)\geq 0\) which is required to hold only for large values of \(| x|\). The nonlinearity \(f\) is radial in the space variable and has to satisfy certain sign and growth properties. It is shown that \(\limsup_{x\to\infty}u(x)| x|^{n-2}<\infty\) holds provided \(u\) is of finite energy. Further results contain a more careful description of this asymptotic behaviour.
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 40244
zbMATH Keywords: semilinear elliptic equations
zbMATH Keywords: radial solutions
zbMATH Keywords: finite energy
zbMATH Keywords: asymptotic behaviour
reviewed by: M. Fuchs
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 40244