Global existence for some integro-differential equations with delay subject to non-local conditions
type: Item
instance of: scholarly article
title: Global existence for some integro-differential equations with delay subject to non-local conditions
zbMATH Open document ID: 1008.45009
DOI: 10.4171/ZAA/1076
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2003-01-28T00:00:00Z
review text: The authors consider the following integro-differential equation in a Banach space: \[ dx(t)/dt=Ax(t)+ F \left(t, x(\sigma_1(t)), \int_0^t g\left(t, s, x(\sigma_2(s)), \int_0^s k(\tau, s, x(\sigma_3(\tau))) d\tau \right) ds\right) \] with the non-local condition \[ x(0) + h (t_1, \dots , t_p, x(.))=x_0\in X. \] Here \(A\) is a generator of a linear strongly continuous semigroup, \(F, g, k, \sigma_j\) and \(h\) are given functions. Conditions for the global existence of solutions to that problem are derived.
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 45J05
zbMATH DE Number: 1779547
zbMATH Keywords: integro-differential equations
zbMATH Keywords: equations with delay
zbMATH Keywords: nonlocal conditions
zbMATH Keywords: global existence
zbMATH Keywords: Banach space
author: Said Mazouzi
author: N.-E. Tatar
reviewed by: Michael I. Gil'
MaRDI profile type: Publication
cites work: Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem
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description: scientific article; zbMATH DE number 1779547