Singular initial value problem for a system of integro-differential equations
type: Item
instance of: scholarly article
title: Singular initial value problem for a system of integro-differential equations
zbMATH Open document ID: 1258.45005
DOI: 10.1155/2012/918281
author: Zdeněk Šmarda
author: Y. Khan
published in: Abstract and Applied Analysis
publication date: 2013-02-04T00:00:00Z
review text: Summary: Analytical properties like existence, uniqueness, and asymptotic behavior of solutions are studied for the following singular initial value problem: \[ g_i(t)y'_i(t) = a_iy_i(t)\left(1 + f_i\left(t, \mathbf{y}(t), \int^t_{0^+} K_i(t, s, \text\textbf{y}(t), \text\textbf{y}(s))ds\right)\right), \quad y_i(0^+) = 0, t \in (0, t_0], \] where \(\mathbf{y} = (y_i, \dots, y_n), a_i > 0, i = 1, \dots, n\) are constants and \(t_0 > 0\). An approach which combines topological method of T. Ważewski and Schauder's fixed point theorem is used. Particular attention is paid to construction of asymptotic expansions of solutions for certain classes of systems of integrodifferential equations in a right-hand neighbourhood of a singular point.
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45G15
Mathematics Subject Classification ID: 45G05
zbMATH DE Number: 6134192
zbMATH Keywords: system of integro-differential equations
zbMATH Keywords: singular initial value problem
Wikidata QID: Q58697095
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/918281
OpenAlex ID: W2115726546
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description: scientific article; zbMATH DE number 6134192