Decreasing streamlines of solutions and spectral properties of linearized operators for semilinear elliptic equations
type: Item
instance of: scholarly article
title: Decreasing streamlines of solutions and spectral properties of linearized operators for semilinear elliptic equations
zbMATH Open document ID: 0685.35044
author: Takashi Suzuki
published in: Proceedings of the Japan Academy. Series A
publication date: 1988-01-01T00:00:00Z
review text: Let \(\Omega\) be the unit ball in \({\mathbb{R}}^ N\), let \(f: {\mathbb{R}}^+\to {\mathbb{R}}^+\) be a \(C^ 1\) function and let u be a positive solution of the semilinear elliptic equation \(-\Delta u=f(u)\) in \(\Omega\), \(u=0\) on \(\partial \Omega\). The author studies the spectrum of the linearized operator \(A=A(u)=-\Delta -f'(u).\) In particular, he proves \(\dim Ker A(u)\leq 1.\) An application to the case \(f(u)=\lambda e^ u\) is given.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 35P30
zbMATH DE Number: 4122458
zbMATH Keywords: positive solution
zbMATH Keywords: semilinear elliptic equation
zbMATH Keywords: linearized operator
MaRDI profile type: Publication
full work available at URL: pjaa.64.315
OpenAlex ID: W2027451179
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DOI: 10.3792/PJAA.64.315
description: scientific article; zbMATH DE number 4122458