Publication detail
Boundary-value problems for weakly nonlinear delay differential systems
BOICHUK, A. DIBLÍK, J. KHUSAINOV, D. RŮŽIČKOVÁ, M.
Original Title
Boundary-value problems for weakly nonlinear delay differential systems
English Title
Boundary-value problems for weakly nonlinear delay differential systems
Type
journal article - other
Language
en
Original Abstract
Conditions are derived of the existence of solutions of nonlinear boundary-value problems for systems of $n$ ordinary differential equations with constant coefficients and single delay (in the linear part) and with a finite number of measurable delays of argument in nonlinearity. The use of a delayed matrix exponential and a method of pseudo-inverse by Moore-Penrose matrices led to an explicit and analytical form of sufficient conditions for the existence of solutions in a given space and, moreover, to the construction of an iterative process for finding the solutions of such problems in a general case when the number of boundary conditions does not coincide with the number of unknowns in the differential system with a single delay.
English abstract
Conditions are derived of the existence of solutions of nonlinear boundary-value problems for systems of $n$ ordinary differential equations with constant coefficients and single delay (in the linear part) and with a finite number of measurable delays of argument in nonlinearity. The use of a delayed matrix exponential and a method of pseudo-inverse by Moore-Penrose matrices led to an explicit and analytical form of sufficient conditions for the existence of solutions in a given space and, moreover, to the construction of an iterative process for finding the solutions of such problems in a general case when the number of boundary conditions does not coincide with the number of unknowns in the differential system with a single delay.
Keywords
Boundary-value problem; r weakly nonlinear delay differential system.
RIV year
2011
Released
01.08.2011
ISBN
1085-3375
Periodical
Abstract and Applied Analysis
Year of study
2011
Number
1
State
US
Pages from
1
Pages to
19
Pages count
19
Documents
BibTex
@article{BUT72868,
author="Alexander {Boichuk} and Josef {Diblík} and Denys {Khusainov} and Miroslava {Růžičková}",
title="Boundary-value problems for weakly nonlinear delay differential systems",
annote="Conditions are derived of the existence of solutions of nonlinear boundary-value problems for systems of $n$ ordinary differential equations with constant coefficients and single delay (in the linear part) and with a finite number of measurable delays of argument in nonlinearity. The use of a delayed matrix exponential and a method of pseudo-inverse by Moore-Penrose matrices led to an explicit and analytical form of sufficient conditions for the existence of solutions in a given space and, moreover, to the construction of an iterative process for finding the solutions of such problems in a general case when the number of boundary conditions does not coincide with the number of unknowns in the differential system with a single delay.",
chapter="72868",
number="1",
volume="2011",
year="2011",
month="august",
pages="1--19",
type="journal article - other"
}