Refined approximations of the solutions of a coupled system with turning points
type: Item
instance of: scholarly article
title: Refined approximations of the solutions of a coupled system with turning points
zbMATH Open document ID: 0732.34023
DOI: 10.1016/0022-0396(91)90067-J
author: N. E. Zubov
published in: Journal of Differential Equations
publication date: 1991-01-01T00:00:00Z
review text: The authors present the asymptotic behavior of solutions of the following boundary value problem \[ u''=v,\quad \epsilon v''+f(u,u')v'- q(x,u,u')v=0,\quad x\in I, \] \[ u(0,\epsilon)=u(1,\epsilon)=0,\quad v(0,\epsilon)=v_ 0,\quad v(1,\epsilon)=v_ 1, \] where \(g(x,u,u')\geq 0\), \(f(u,u')\) has turning points on I, and \(\epsilon\) is a small parameter. They provide upper and lower solutions, \(\beta\) (x,\(\epsilon\)) and \(\alpha\) (x,\(\epsilon\)), exhibiting boundary layer and interior layer behavior, for which \(\lim_{\epsilon \to 0+}(\beta (x,\epsilon)-\alpha (x,\epsilon))=0,\) uniformly on I.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34E20
zbMATH DE Number: 4210574
zbMATH Keywords: coupled systems
zbMATH Keywords: turning points
zbMATH Keywords: limiting behavior
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: boundary value problem
zbMATH Keywords: upper and lower solutions
reviewed by: Abdelkader Boucherif
MaRDI profile type: Publication
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full work available at URL: 0022-0396(91)90067-j
OpenAlex ID: W2022470442
description: scientific article; zbMATH DE number 4210574