First-order ordinary differential equations with several bounded separate solutions
type: Item
instance of: scholarly article
title: First-order ordinary differential equations with several bounded separate solutions
zbMATH Open document ID: 0914.34033
author: Antonio Tineo
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-06-16T00:00:00Z
full work available at URL: http://www.saber.ula.ve/handle/123456789/22652
review text: The author deals with the equation (1) \(x'= F(t,x)+\lambda\), where \(F: \mathbb{R}\times \mathbb{R}\to \mathbb{R}\) is a continuous function, \(F(t,x)\to -\infty\) as \(| x|\to \infty\) uniformly on \(t\in\mathbb{R}\), and \(F(t,x)\) is either bounded on \(\mathbb{R}\times K\) for each compact set \(K\subset \mathbb{R}\) or \(T\)-periodic in \(t\) for some \(T>0\). The existence and the number of bounded or separate or singular solutions to (1) are discussed according to \(\lambda\in\mathbb{R}\). The obtained results are compared with those of \textit{J. Mawhin} [Z. Angew. Math. Phys. 38, 257-265 (1987; Zbl 0644.34035)].
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 1218226
zbMATH Keywords: boundedness
zbMATH Keywords: existence
zbMATH Keywords: bounded
zbMATH Keywords: separate
zbMATH Keywords: singular solutions
reviewed by: Jan Ohriska
MaRDI profile type: Publication
OpenAlex ID: W2067515599
cites work: First order ordinary differential equations with several periodic solutions
cites work: Asymptotic behaviour of positive solutions of the nonautonomous Lotka- Volterra competition equations
cites work: An iterative scheme for the \(N\)-competing species problem
DOI: 10.1006/JMAA.1998.5920
description: scientific article; zbMATH DE number 1218226