Entire bounded solutions for a class of sublinear elliptic equations
type: Item
instance of: scholarly article
title: Entire bounded solutions for a class of sublinear elliptic equations
zbMATH Open document ID: 1096.35045
author: K. El Mabrouk
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-08-19T00:00:00Z
review text: The author deals with the question of the existence of a bounded solution to the sublinear elliptic problem \[ \begin{cases} \Delta u=\xi(x) u^\gamma\text{ in }\mathbb{R}^N\\ u\geq 0,\;u\not\equiv 0,\end{cases}\tag{1} \] where \(\xi\in L^\infty_{\text{loc}} (\mathbb{R}^N)\) is nonnegative, \(\gamma \in[0,1]\), and \(\Delta\) denotes as usually the Laplacian on \(\mathbb{R}^N\). By means of thinness at \(\infty\), the author gives a characterization of all functions \(\xi\) for which problem (1) possesses a bounded solution. The author studies (1) for a subdomain \(\Omega\) of \(\mathbb{R}^N\) and establishes necessary and sufficient conditions under which there exists bounded solutions to (1) replacing \(\mathbb{R}^N\) by \(\Omega\).
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 2093000
zbMATH Keywords: Sublinear Dirichlet problem
zbMATH Keywords: Thickness and thinness at \(\infty\)
zbMATH Keywords: Green domain
zbMATH Keywords: Green function
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.na.2004.01.004
OpenAlex ID: W1990689844
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DOI: 10.1016/J.NA.2004.01.004
description: scientific article; zbMATH DE number 2093000