Impulsive retarded differential equations in Banach spaces via Bochner-Lebesgue and Henstock integrals
type: Item
instance of: scholarly article
title: Impulsive retarded differential equations in Banach spaces via Bochner-Lebesgue and Henstock integrals
zbMATH Open document ID: 1011.34070
DOI: 10.1016/S0362-546X(01)00769-6
author: Plácido Zoega Táboas
author: M. Federson
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-08-25T00:00:00Z
review text: By means of the integral of Henstock, the authors provide conditions for the existence and uniqueness of solutions as well as continuous dependence on the initial conditions of the system \[ x'(t)=f(t,x_{t}), \quad t\not=t_{k}, \quad k=1,\ldots,m,\quad \Delta x(t_{k})=I_{k}(x(t_{k})), \quad k=1,\dots,m,\;x_{0}=\phi, \] where \(\phi\) is a given continuous function defined on \([-r,t_{0}], \;r\geq 0, \;f\) is a continuous map from an open set \(\Omega\subset \mathbb{R}\times C([-r,t_{0}],X),\) \(t_{k}, \;k=1,\dots,m\), are pre-assigned moments of impulses from the interval \([t_{0},t_{0}+a], \;a\geq 0, \;x\to I_{k}(x)\) maps the Banach space \(X\) into itself and \(\Delta x(t_{k}):=x(t_{k}^{+})-x(t_{k}^{-}), \;k=1,\dots, m.\)
Mathematics Subject Classification ID: 34K45
Mathematics Subject Classification ID: 34K30
zbMATH DE Number: 1788019
zbMATH Keywords: retarded equations
zbMATH Keywords: impulses
zbMATH Keywords: Henstock integrals
zbMATH Keywords: existence theorems
reviewed by: Mouffak Benchohra
MaRDI profile type: Publication
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full work available at URL: s0362-546x(01)00769-6
OpenAlex ID: W2009617258
description: scientific article; zbMATH DE number 1788019