On a nonlinear eigenvalue problem in ODE
type: Item
instance of: scholarly article
title: On a nonlinear eigenvalue problem in ODE
zbMATH Open document ID: 1073.34051
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-03-08T00:00:00Z
review text: The author studies the following variant of the logistic differential equation with diffusion \[ -du''(x)=g(x)u(x)-u^2(x)\text{ for }x\in\mathbb{R}, \] where \(d\) is a positive parameter and \(g\) is a smooth function. As the main result he proves that if \(g(x)<0\) in a neighborhood of infinity, then every positive solution \(u\) must tend to zero as \(| x|\to\infty\).
reviewed by: Ludvík Janoš
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 2141760
zbMATH Keywords: subsolutions
zbMATH Keywords: supersolutions
zbMATH Keywords: principal eigenvalue
zbMATH Keywords: variational characterizations
author: Ghasem A. Afrouzi
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.08.040
OpenAlex ID: W2039094635
cites work: On a diffusive logistic equation
cites work: On the existence of positive eigenfunctions for an eigenvalue problem with indefinite weight function
cites work: On the construction of super and subsolutions for elliptic equations on all of N
cites work: Ecological models, permanence and spatial heterogeneity
cites work: Linear and Semilinear Parabolic Equations on BUC(ℝN)
cites work: Long-time behaviour for reaction-diffusion equations on
DOI: 10.1016/J.JMAA.2004.08.040
description: scientific article; zbMATH DE number 2141760