Delay integro-differential inequalities with initial time difference and applications
type: Item
instance of: scholarly article
title: Delay integro-differential inequalities with initial time difference and applications
zbMATH Open document ID: 1054.45004
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-06-15T00:00:00Z
review text: The author considers initial value problems of differential equations relative to the changes in the initial time. He introduces the operator \[ Fx(t;t_0)=f(t,x(t),x(\alpha(t-t_0)+t_0))+\int^t_{t_0}H(t,s,x(s),x(\beta(s-t_0)+t_0))\,ds \] and formulates two problems: \[ x'(t)=Fx(t;t_0),\quad t\in [t_0,t_0+T],\;x(t_0)=\overline\kappa \] \(x'(t)=Fx(t;t_0)\), \(t\in[\tau_0,\tau_0+T]\), \(x(\tau_0)=\overline\kappa\) for some fixed positive \(T>0\), where the functions \(f,F,\alpha,\beta\) are prescribed. In Section 2 some comparison results are formulated to compare any two solutions of corresponding delay integro-differential inequalities with initial time difference. In Section 3, the author uses the monotone iterative technique to delay integro-differential equations. The existence of extremal solutions ist obtained. Section 5 contains some existence results when there are several delayed arguments on the right hand side of \(F\). Illustrative examples are presented in Section 4.
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 34K05
Mathematics Subject Classification ID: 34K12
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 2075646
zbMATH Keywords: Delay integro-differential inequalities
zbMATH Keywords: Delay integro-differential equations
zbMATH Keywords: Monotone iterative technique
zbMATH Keywords: extremal solutions
zbMATH Keywords: existence
zbMATH Keywords: initial value problems
author: Tadeusz Jankowski
reviewed by: Vasil G. Angelov
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.11.036
OpenAlex ID: W1985509927
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DOI: 10.1016/J.JMAA.2003.11.036
description: scientific article; zbMATH DE number 2075646