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

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

Pages from

1

Pages to

19

Pages count

19

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"
}