Detail publikačního výsledku

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

Peer-reviewed article not indexed in WoS or Scopus

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.

Key words in English

Boundary-value problem; r weakly nonlinear delay differential system.

Authors

BOICHUK, A.; DIBLÍK, J.; KHUSAINOV, D.; RŮŽIČKOVÁ, M.

RIV year

2012

Released

01.08.2011

ISBN

1085-3375

Periodical

Abstract and Applied Analysis

Volume

2011

Number

1

State

United States of America

Pages from

1

Pages to

19

Pages count

19

Full text in the Digital Library

http://hdl.handle.net/

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",
  journal="Abstract and Applied Analysis",
  year="2011",
  volume="2011",
  number="1",
  pages="1--19",
  issn="1085-3375"
}