\(L_ p\)-equivalence of impulsive equations
type: Item
instance of: scholarly article
title: \(L_ p\)-equivalence of impulsive equations
zbMATH Open document ID: 0671.34067
DOI: 10.1007/BF00671319
published in: International Journal of Theoretical Physics
publication date: 1988-01-01T00:00:00Z
review text: In a Banach space X, consider the differential equation with impulses \(dx/dt=F(t,x)\), \(x(t_ n+0)=Q_ nx(t_ n)\), with the given infinite sequence \(t_ n\to \infty\). The function F is assumed continuous and the operators \(Q_ n\) are bounded linear. Consider also another similar system, as ``perturbed system''; these two systems are called \(L_ p\)- equivalent if, within some specified neighborhoods, for each solution of the first system there is a solution of the second system such that the difference is \(L_ p\)-integrable. The two systems are called asymptotically \(L_ p\)-equivalent if this happens in some interval \((t_ 0,\infty)\). This paper gives a set of sufficient conditions for two such systems to be \(L_ p\)-equivalent and to be asymptotically \(L_ p\)-equivalent. It discusses these conditions and hints at possible extensions.
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 34C20
zbMATH DE Number: 4097868
zbMATH Keywords: impulsive differential equations
zbMATH Keywords: integral equivalence
zbMATH Keywords: Banach
zbMATH Keywords: spaces
zbMATH Keywords: Lp equivalence of systems
zbMATH Keywords: perturbed system
author: Drumi Bainov
author: S. Kostadinov
author: Peter P. Zabreĭko
MaRDI profile type: Publication
cites work: Q3244654
cites work: Asymptotic equivalence of nonlinear systems
cites work: Q3342953
description: scientific article; zbMATH DE number 4097868