Positive solutions of semilinear elliptic problems in unbounded domains
type: Item
instance of: scholarly article
title: Positive solutions of semilinear elliptic problems in unbounded domains
zbMATH Open document ID: 0583.35039
DOI: 10.1016/0022-0396(85)90061-0
author: E. S. Noussair
author: Charles A. Swanson
published in: Journal of Differential Equations
publication date: 1985-01-01T00:00:00Z
review text: In this paper boundary value problems of the type \(Lu=f(x,u)\) in D, \(u=0\) on \(\partial D\) are considered where L is a second order uniformly elliptic differential operator in divergence form, f(x,t) has polynomial growth in t, and D is unbounded. By means of variational methods a sequence of positive solutions \(u_ n\) is constructed in bounded subdomains \(D_ n\subset D\), vanishing on \(\partial D_ n\). By compactness arguments it is then shown that there exists a subsequence converging, locally uniformly in \(C^ 2(D)\), to a positive solution in the whole domain D. The behaviour of this solution as \(| x| \to \infty\) is also studied.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35A15
zbMATH DE Number: 3933606
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: second order uniformly elliptic differential operator
zbMATH Keywords: divergence form
zbMATH Keywords: positive solutions
reviewed by: Catherine Bandle
MaRDI profile type: Publication
full work available at URL: 0022-0396(85)90061-0
OpenAlex ID: W2011051924
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description: scientific article; zbMATH DE number 3933606