Comparison theorems for radial solutions of semilinear elliptic equations
type: Item
instance of: scholarly article
title: Comparison theorems for radial solutions of semilinear elliptic equations
zbMATH Open document ID: 0667.35021
DOI: 10.1016/0022-0396(88)90159-3
published in: Journal of Differential Equations
publication date: 1988-01-01T00:00:00Z
review text: Radially symmetric solutions to the elliptic equation \[ (E1)\quad \Delta u+f(u)=0 \] satisfy the ordinary differential equation \[ (E2)\quad u_{rr}+((n-1)/r)u_ r+f(u)=0,\quad u_ r(0)=0, \] where \(r=| x|\) and \(x\in {\mathbb{R}}^ n\). Let \(f(u)=u[1+g(u)]\), where g is even, positive and monotonically increasing. The author obtains a priori bounds for solutions of (E2) and studies the location of zeros as well as behavior of solutions for large r. The results are applied to the eigenvalue problem \[ \Delta w+\lambda w(1+| w|^{p-1})=0,\quad x\in \Omega;\quad w=0\quad on\quad \partial \Omega. \]
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 35A30
zbMATH DE Number: 4091981
zbMATH Keywords: Radially symmetric
zbMATH Keywords: a priori bounds
zbMATH Keywords: location of zeros
zbMATH Keywords: eigenvalue problem
author: C. J. Budd
MaRDI profile type: Publication
full work available at URL: 0022-0396(88)90159-3
OpenAlex ID: W2084333204
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description: scientific article; zbMATH DE number 4091981