Existence and uniqueness of solution of the Cauchy problem for singular systems of integro-differential equations
type: Item
instance of: scholarly article
title: Existence and uniqueness of solution of the Cauchy problem for singular systems of integro-differential equations
zbMATH Open document ID: 0824.45008
DOI: 10.1007/BF01061366
published in: Ukrainian Mathematical Journal
publication date: 1995-03-20T00:00:00Z
review text: Consider the system of singular integro-differential equations \[ y'= f(x, y)+ \int^ x_{0^ +} g(x, s, y(s))ds\tag{1} \] with the initial condition \(y(0^ +)= 0\), where \(y\), \(f\), and \(g\) are vector functions. The author establishes sufficient conditions for the existence of a unique solution of problem (1) in the indicated region. As an application, the asymptotics of solutions of a system of singular integro-differential equations are also investigated.
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45G15
Mathematics Subject Classification ID: 45M05
zbMATH DE Number: 726974
zbMATH Keywords: Cauchy problem
zbMATH Keywords: uniqueness
zbMATH Keywords: existence
zbMATH Keywords: asymptotics
zbMATH Keywords: system of singular integro-differential equations
author: Zdeněk Šmarda
reviewed by: Zhicheng Wang
MaRDI profile type: Publication
cites work: Q3754919
cites work: Existence and asymptotic behavior of solutions of a real system of differential equations near a singular point
full work available at URL: https://doi.org/10.1007/bf01061366
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description: scientific article; zbMATH DE number 726974