About power absolute integrated of the solution of Volterra system of linear second kind integral equations on half-axis
type: Item
instance of: scholarly article
title: About power absolute integrated of the solution of Volterra system of linear second kind integral equations on half-axis
zbMATH Open document ID: 1473.45004
DOI: 10.1134/S1995080221030100
author: S. Iskandarov
published in: Lobachevskii Journal of Mathematics
publication date: 2021-05-20T00:00:00Z
review text: The author investigates the solvability condition of the following system of Volterra integral equation \[ x(t) + \int_{t_0}^t[K(t,\tau) + Q(t,\tau)]x(\tau)d\tau = f(t) + q(t), \qquad t \geqslant t_0, \] with an unknown vector-function \(x(t)=(x_1(t),\ldots,x_n(t))^\top\), vector right-hand sides \(f(t)\), \(q(t)\) and matrix functions (kernels) \(K(t,\tau)\), \(Q(t,\tau)\). Two lemmas are proved and, by imposing several conditions on the data of the equation, the author states (without proof) the existence of a solution to the above equation in the spaces \(L^1(I)\) and in \(L^2(I)\), \(I=[t_0,\infty)\). A concrete example is presented.
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 45F05
zbMATH DE Number: 7350131
zbMATH Keywords: system of Volterra type equations of second kind
zbMATH Keywords: weight functions
zbMATH Keywords: truncating functions
zbMATH Keywords: sufficient conditions for solvability
reviewed by: Roland Duduchava
MaRDI profile type: Publication
cites work: Q5756777
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cites work: Volterra integral equations
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full work available at URL: s1995080221030100
OpenAlex ID: W3158678486
description: scientific article; zbMATH DE number 7350131