Topological structure of solution sets to asymptotic boundary value problems
type: Item
instance of: scholarly article
title: Topological structure of solution sets to asymptotic boundary value problems
zbMATH Open document ID: 1188.34015
author: Jan Andres
author: Martina Pavlačková
published in: Journal of Differential Equations
publication date: 2009-12-22T00:00:00Z
review text: The paper studies the topological structure of the solutions set to the semi-linear problem \[ \ddot x(t)+A(t)\dot x(t)+B(t)x(t)\in C(t,x(t),x\dot (t)),\quad l(x,\dot x)=0 \tag{1} \] on the compact interval \([0,m]\), where \(A\), \(B\) are Lebesgue integrable matrix functions, \(C\) is an upper-Carathéodory mapping and \(l\) is a linear bounded operator. The authors prove that the set of solutions of (1) is a nonempty, compact \(AR\)-space. Then, by means of the inverse limit method, problem (1) is investigated on the non-compact interval \([t_0,\infty]\) and it is proved that the set of its solutions is an \(R_\delta\)-set. The information about the structure is employed for obtaining an existence result for nonlinear asymptotic problems. Some illustrating examples are supplied.
reviewed by: Irena Rachůnková
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B40
Mathematics Subject Classification ID: 47H04
zbMATH DE Number: 5651185
zbMATH Keywords: asymptotic problems
zbMATH Keywords: vector differetial systems
zbMATH Keywords: topological structure
zbMATH Keywords: \(R_\delta\)-set
zbMATH Keywords: inverse limit
zbMATH Keywords: existence result
MaRDI profile type: Publication
full work available at URL: j.jde.2009.08.010
OpenAlex ID: W2036040938
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DOI: 10.1016/J.JDE.2009.08.010
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description: scientific article; zbMATH DE number 5651185