Non-autonomous nonlinear integro-differential equations with infinite delay
type: Item
instance of: scholarly article
title: Non-autonomous nonlinear integro-differential equations with infinite delay
zbMATH Open document ID: 1163.45007
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-03-25T00:00:00Z
review text: The authors prove the local existence and uniqueness of strict solutions of the nonlinear functional integro-differential problem with infinite delay \[ \begin{cases} u'(t)=A(t)u(t)+\int_0^tk(t,s,u(s))\,ds+F(t,u_t),\quad 0\leq t\leq T,\\ u_0=\varphi\in\mathcal P,\end{cases} \] in a Banach space \(E\), where \((A(t))_{0\leq t\leq T}\) is a family of linear operators defined on a non-dense set \(D\) of \(E\), \(k\in C(\Delta(0,T)\times D,E)\), \(F\in C^1([0,T]\times {\mathcal P}, E)\), and the phase space \((\mathcal P,\|\cdot\|_{\mathcal P})\) is the Banach space of functions from \((-\infty,0]\) into \(E\), which satisfy some assumptions. Three other related functional integro-differential problems are also investigated.
reviewed by: Rodica Luca
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 5532910
zbMATH Keywords: nonlinear functional integro-differential equation
zbMATH Keywords: infinite delay
zbMATH Keywords: phase space
zbMATH Keywords: strict solution
zbMATH Keywords: Banach space
author: Dhirendra Bahuguna
author: Dwijendra N. Pandey
author: Amit Ujlayan
MaRDI profile type: Publication
full work available at URL: j.na.2008.03.051
OpenAlex ID: W2021603696
cites work: Local existence and stability for some partial functional-differential equations with infinite delay
cites work: Existence for a class of partial functional differential equations with infinite delay
cites work: Solutions to non-autonomous integrodifferential equations with infinite delay
cites work: Local existence for nonlinear Volterra integrodifferential equations with infinite delay
cites work: Local existence for retarded Volterra integrodifferential equations with Hille--Yosida operators
cites work: Q4444859
cites work: Q4163814
cites work: Functional differential equations with infinite delay
cites work: Some considerations to the fundamental theory of infinite delay equations
cites work: Q5627250
cites work: Q4214732
cites work: Nonlinear hyperbolic volterra integrodifferential equations
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: Non autonomous evolution operators of hyperbolic type
cites work: Q3797548
cites work: Existence and continuous dependence for functional-differential equations with unbounded delay
cites work: Q3207428
cites work: Existence and Stability for Partial Functional Differential Equations
cites work: A note on semilinear abstract functional differential and integrodifferential equations with infinite delay.
cites work: Extrapolation methods to solve non-autonomous retarded partial differential equations
DOI: 10.1016/J.NA.2008.03.051
description: scientific article; zbMATH DE number 5532910