Decaying solutions for semilinear elliptic equations in exterior domains
type: Item
instance of: scholarly article
title: Decaying solutions for semilinear elliptic equations in exterior domains
zbMATH Open document ID: 0956.35049
DOI: 10.12775/TMNA.1999.039
author: Robert Stańczy
published in: Topological Methods in Nonlinear Analysis
publication date: 2001-02-28T00:00:00Z
review text: The author considers the following problem \[ \begin{gathered} -\Delta u = f(\|x\|,u)\quad\text{for}\quad \|x\|\geq 1,\quad x\in\mathbb R^n, \quad n\geq 3\\ u(x) = 0 \quad\text{for}\quad \|x\|= 1,\quad \lim_{\|x\|\to\infty} u(x) = 0. \end{gathered} \] It is proved the existence of at least one radial solution. Typified nonlinearities: \(f(r,v) = h(r)g(v)\), where \(h: [1,\infty)\rightarrow\mathbb R\) and \(g: \mathbb R\rightarrow\mathbb R\) are continuous, and (a) \(|h(r)|\leq\text{const}\cdot r^\beta\), \(\beta<-2\); (b) \(g(0)\neq 0\); (c) \(\varlimsup_{|v|\to\infty}|g(v)|/|v|< C\), where \(C\) is an explicitly defined constant; or (\(\text{c}'\)) \(g(v)v< 0\) at large \(|v|\).
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 34B27
zbMATH DE Number: 1507588
zbMATH Keywords: semilinear elliptic equations
zbMATH Keywords: exterior domain
zbMATH Keywords: Green function
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1507588