Existence results for partial neutral functional integrodifferential equations with unbounded delay
type: Item
instance of: scholarly article
title: Existence results for partial neutral functional integrodifferential equations with unbounded delay
zbMATH Open document ID: 1056.45012
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-06T00:00:00Z
review text: Assume that \(A\) is a (possibly unbounded) infinitesimal generator of an analytic semigroup of bounded linear operators \((T(t))_{t\geq 0}\) on a Banach space \(X\). The author studies the existence of mild solutions of the partial neutral functional integrodifferential equation with unbounded delay having the form \[ {d\over dt}(x(t)+ G(t, x_t))= Ax(t)+ F\Biggl(t, x_t,\int^t_0 h(t,x,x_s)\,ds\Biggr)\,(\text{for }t\in I= [\delta, T]),\, x(\delta)= \varphi.\tag{1} \] Here the history \(x_t:(-\infty, 0]\to X\), \(x_t(s)= x(t+ s)\) is assumed to belong to some abstract phase space \(B\) defined axiomatically. There are imposed some other regularity assumptions on the components of the problem (1). The existence result concerning (1) is obtained with help of the Leray-Schauder alternative. Some applications are also given.
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 2081790
zbMATH Keywords: partial neutral functional integrodifferential equations
zbMATH Keywords: unbounded delay
zbMATH Keywords: analytic semigroup of bounded linear operators
zbMATH Keywords: Banach space
zbMATH Keywords: mild solutions
zbMATH Keywords: Leray-Schauder alternative
zbMATH Keywords: fractional powers of closed operators
author: Eduardo Hernández
reviewed by: Józef Banaś
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.11.052
OpenAlex ID: W4242378265
cites work: Existence of solutions of nonlinear neutral integrodifferential equations in Banach spaces
cites work: Q4421936
cites work: Q4163814
cites work: Introduction to functional differential equations
cites work: Q4313423
cites work: Existence of periodic solutions of partial neutral functional differential equations with unbounded delay
cites work: Existence results for partial neutral functional differential equations with unbounded delay
cites work: Functional differential equations with infinite delay
cites work: Q4063689
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: Q5551837
DOI: 10.1016/J.JMAA.2003.11.052
description: scientific article; zbMATH DE number 2081790