On connection between second-order delay differential equations and integrodifferential equations with delay
type: Item
instance of: scholarly article
title: On connection between second-order delay differential equations and integrodifferential equations with delay
zbMATH Open document ID: 1195.34094
DOI: 10.1155/2010/143298
author: Josef Diblík
author: Leonid Berezansky
author: Zdeněk Šmarda
published in: Advances in Difference Equations
publication date: 2010-04-08T00:00:00Z
review text: The second order delay differential equation \[ x''(t) + a(t)x'(g(t))+b(t)x(h(t)) = 0 \] appears in many applications. One of the methods used in the study of this equation is to transform it to a first order differential or integrodifferential equation with delays. As a result of such a transformation, the initial value problem of \[ x'(t) + \int^t_{t_0}K(t, s)x(h(s))ds = f(t),\quad t\geq t_0,\quad x\in\mathbb R^n,\;x(t) = \varphi(t),\;t < t_0 \] arises. In this paper, the existence and uniqueness of a solution to the above initial value problem is studied and a representation formula for the solution is provided. This work is a continuation of previous work involving the first author.
reviewed by: Zhanyuan Hou
Mathematics Subject Classification ID: 34K05
zbMATH DE Number: 5690835
zbMATH Keywords: initial value problem
zbMATH Keywords: delay differential equations
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2010/143298
OpenAlex ID: W2017305626
Wikidata QID: Q59219590
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description: scientific article; zbMATH DE number 5690835