The effect of varying coefficients on the dynamics of a class of superlinear indefinite reaction-diffusion equations
type: Item
instance of: scholarly article
title: The effect of varying coefficients on the dynamics of a class of superlinear indefinite reaction-diffusion equations
zbMATH Open document ID: 0965.35061
published in: Journal of Differential Equations
publication date: 2001-03-13T00:00:00Z
review text: The paper deals with the analysis of the structure of the set of positive solutions of \[ -\Delta u=\lambda u-a(x)|u^p|u\quad \text{in }\Omega,\qquad u|_{\partial\Omega}=0, \] where \(\Omega\) is a bounded \(C^2\) domain of \({\mathbb R}^n\), \( N\geq 1,\) \(\lambda \in {\mathbb R}\) is regarded as a continuation parameter and \(p\in (0,\infty).\) The problem possesses a unique positive solution which is linearly asymptotically stable if the trivial state is linearly unstable and the model admits some positive solution.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B60
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 1529993
zbMATH Keywords: reaction-diffusion equations
zbMATH Keywords: positive solutions
author: R. Gómez-Reñasco
author: Julián López-Gómez
reviewed by: G. Jaiani
MaRDI profile type: Publication
full work available at URL: jdeq.2000.3772
OpenAlex ID: W2092328240
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DOI: 10.1006/JDEQ.2000.3772
description: scientific article; zbMATH DE number 1529993