Perturbed Fredholm boundary value problems for delay differential systems
type: Item
instance of: scholarly article
title: Perturbed Fredholm boundary value problems for delay differential systems
zbMATH Open document ID: 1077.34069
DOI: 10.1155/S1085337503304026
author: Myron K. Grammatikopoulos
author: Alexander Boichuk
published in: Abstract and Applied Analysis
publication date: 2005-04-29T00:00:00Z
full work available at URL: https://eudml.org/doc/51877
review text: The considered linear boundary value problem with a small parameter \(\varepsilon\) has the form \[ \dot z(t)=\sum^k_{i=1} A_i(t)z(h_i(t))+\varepsilon\sum^k_{i=1}B_i(t)z(h_i(t))+g(t),\quad t\in [a,b];\;z(s)=\psi(s), \;s<\alpha; \;\ell z=\alpha. \] The unknown solution \(z\) takes values in a finite-dimensional space. The functions \(h_i(t)\leq t\) are measurable. In case \(h_i(t)<\alpha\), it is assumed that \(z(h_i(t))=\psi(h_i(t))\). The boundary conditions are described by the bounded linear operator \(\ell\). The Fredholm properties of the boundary value problem are obtained in the form of power series in \(\varepsilon\). Examples are given.
reviewed by: Sergei A. Brykalov
Mathematics Subject Classification ID: 34K10
Mathematics Subject Classification ID: 34K06
zbMATH DE Number: 2163619
zbMATH Keywords: linear boundary value problem
zbMATH Keywords: linear functional-differential equation
zbMATH Keywords: small parameter
MaRDI profile type: Publication
OpenAlex ID: W2062009035
description: scientific article; zbMATH DE number 2163619