Dependence on the parameters of the set of trajectories of the control system described by a nonlinear Volterra integral equation.
type: Item
instance of: scholarly article
title: Dependence on the parameters of the set of trajectories of the control system described by a nonlinear Volterra integral equation.
zbMATH Open document ID: 1340.45007
author: Anar Huseyin
author: Nesir Huseyin
published in: Applications of Mathematics
publication date: 2014-10-29T00:00:00Z
full work available at URL: http://hdl.handle.net/10338.dmlcz/143774
review text: This paper addresses the nonlinear Volterra equation \[ x(t) = a(t,x(t))+\lambda \int_{t_0}^t K(t,s,x(s),u(s))\,ds, \] where \(u(t)\) is a known function from the closed ball centered at the origin with radius \(\mu\) in \(L_p\) and the kernel is assumed to be Lipschitz continuous. It is proved that the equation has Lipschitz continuous solutions with respect to \(\mu\) for each fixed \(p\), and is continuous with respect to \(p\) for each fixed \(\mu\). For the theory of the nonlinear Volterra equation, readers may also refer to the monograph of \textit{D. Sidorov} [Integral dynamical models. Singularities, signals and control. Hackensack, NJ: World Scientific (2015; Zbl 1311.45012)].
reviewed by: Denis Sidorov
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 6362228
zbMATH Keywords: nonlinear Volterra integral equation
zbMATH Keywords: control system
zbMATH Keywords: integral constraint
zbMATH Keywords: Lipschitz continuous solutions
MaRDI profile type: Publication
OpenAlex ID: W2070384845
cites work: On a reliable solution of a Volterra integral equation in a Hilbert space.
cites work: Approximation of the attainable sets of the nonlinear control systems with integral constraint on controls
cites work: On the continuity properties of the attainable sets of nonlinear control systems with integral constraint on controls
cites work: On the continuity property of \(L_{p}\) balls and an application
cites work: Reliable solutions of problems in the deformation theory of plasticity with respect to uncertain material function
cites work: PRECOMPACTNESS OF THE SET OF TRAJECTORIES OF THE CONTROLLABLE SYSTEM DESCRIBED BY A NONLINEAR VOLTERRA INTEGRAL EQUATION
cites work: Q5848440
cites work: Q5559800
cites work: Q3209190
cites work: Q3894443
cites work: Q5839225
cites work: Q3966605
cites work: Q4393445
cites work: Q4937534
DOI: 10.1007/S10492-014-0056-4
description: scientific article; zbMATH DE number 6362228