Nonlinear elliptic problems in annular domains
type: Item
instance of: scholarly article
title: Nonlinear elliptic problems in annular domains
zbMATH Open document ID: 0618.35043
DOI: 10.1016/0022-0396(87)90123-9
published in: Journal of Differential Equations
publication date: 1987-01-01T00:00:00Z
review text: This paper deals with positive radially symmetric solutions of \(\Delta u+f(u)=0\) in \(R_ 1<| x| <R_ 0\), \(x\in R^ N\), \(N\geq 3\) with Dirichlet boundary conditions, or with Neumann boundary conditions on one boundary sphere and Dirichlet conditions on the other. The nonlinearity f satisfies \(f(0)=0\), f is nondecreasing in (0,\(\infty)\), \(\lim_{t\to 0}f(t)/t=0,\lim_{t\to \infty}f(t)/t=\infty.\) Various existence results are obtained by a shooting method combined with comparison theorems and estimates for eigenvalues. We also prove uniqueness results which yield additional information on the solutions. Moreover we formulate a conjecture and prove the first half at the final section.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35P15
zbMATH DE Number: 4002627
zbMATH Keywords: semilinear elliptic
zbMATH Keywords: positive radially symmetric solutions
zbMATH Keywords: Dirichlet boundary conditions
zbMATH Keywords: Neumann boundary conditions
zbMATH Keywords: existence
zbMATH Keywords: shooting method
zbMATH Keywords: comparison theorems
zbMATH Keywords: estimates for eigenvalues
zbMATH Keywords: uniqueness
author: Catherine Bandle
author: Charles V. Coffman
author: Moshe Marcus
MaRDI profile type: Publication
full work available at URL: 0022-0396(87)90123-9
OpenAlex ID: W2077130143
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cites work: Q5516356
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description: scientific article; zbMATH DE number 4002627