A generalized Green operator for a boundary value problem with impulse action
type: Item
instance of: scholarly article
title: A generalized Green operator for a boundary value problem with impulse action
zbMATH Open document ID: 1007.34028
DOI: 10.1023/A:1012440123296
published in: Differential Equations
publication date: 2003-03-27T00:00:00Z
review text: The author considers a linear nonhomogeneous differential equation with impulses of the form \[ {dz\over dt}= A(t) z+ f(t),\quad t\neq\tau_i,\tag{1} \] \[ \ell_i z(\cdot)= a_i,\quad i= 1,\dots, P,\tag{2} \] where \(A(t)\) is a continuous \(n\times n\)-matrix on \([a,b]\); \(f(t)\) is an \(n\)-vector function, continuous for \(t\neq \tau_i\) and has jump discontinuities at the points \(\tau_i\); \(a_i\) and \(c\) are constants. Necessary and sufficient conditions for the solvability of (1), (2) in the case \(\ell_i= \ell\), \(i= 1,\dots, P\), and \(a_i= \alpha\), \(\alpha\in \mathbb{R}^m\), \(m\geq n\), \(i= 1,\dots, P\), are derived.
reviewed by: S. Kostadinov
Mathematics Subject Classification ID: 34B37
Mathematics Subject Classification ID: 34B27
zbMATH DE Number: 1758743
zbMATH Keywords: linear impulse differential equations
zbMATH Keywords: Green operator
author: S. M. Chujko
MaRDI profile type: Publication
full work available at URL: a:1012440123296
OpenAlex ID: W95789214
description: scientific article; zbMATH DE number 1758743