On a two point linear boundary value problem for system of ODEs with deviating arguments

Jan Kubalčík

Archivum Mathematicum (2002)

  • Volume: 038, Issue: 2, page 101-118
  • ISSN: 0044-8753

Abstract

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Two point boundary value problem for the linear system of ordinary differential equations with deviating arguments x ' ( t ) = A ( t ) x ( τ 11 ( t ) ) + B ( t ) u ( τ 12 ( t ) ) + q 1 ( t ) , u ' ( t ) = C ( t ) x ( τ 21 ( t ) ) + D ( t ) u ( τ 22 ( t ) ) + q 2 ( t ) , α 11 x ( 0 ) + α 12 u ( 0 ) = c 0 , α 21 x ( T ) + α 22 u ( T ) = c T is considered. For this problem the sufficient condition for existence and uniqueness of solution is obtained. The same approach as in [2], [3] is applied.

How to cite

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Kubalčík, Jan. "On a two point linear boundary value problem for system of ODEs with deviating arguments." Archivum Mathematicum 038.2 (2002): 101-118. <http://eudml.org/doc/248944>.

@article{Kubalčík2002,
abstract = {Two point boundary value problem for the linear system of ordinary differential equations with deviating arguments \[\{\{x\}^\{\prime \}(t) =\{A\}(t)\{x\}(\tau \_\{11\}(t))+\{B\}(t)\{u\}(\tau \_\{12\}(t)) +\{q\}\_1(t)\,, \{u\}^\{\prime \}(t) =\{C\}(t)\{x\}(\tau \_\{21\}(t))+\{D\}(t)\{u\}(\tau \_\{22\}(t)) +\{q\}\_2(t)\,, \alpha \_\{11\} \{x\}(0) + \alpha \_\{12\} \{u\}(0) = \{c\}\_0, \quad \alpha \_\{21\} \{x\}(T) + \alpha \_\{22\} \{u\}(T) = \{c\}\_T\} \] is considered. For this problem the sufficient condition for existence and uniqueness of solution is obtained. The same approach as in [2], [3] is applied.},
author = {Kubalčík, Jan},
journal = {Archivum Mathematicum},
keywords = {existence and uniqueness of solution; two point linear boundary value problem; linear system of ordinary differential equations; deviating argument; delay; existence; uniqueness; two-point linear boundary value problem},
language = {eng},
number = {2},
pages = {101-118},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On a two point linear boundary value problem for system of ODEs with deviating arguments},
url = {http://eudml.org/doc/248944},
volume = {038},
year = {2002},
}

TY - JOUR
AU - Kubalčík, Jan
TI - On a two point linear boundary value problem for system of ODEs with deviating arguments
JO - Archivum Mathematicum
PY - 2002
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 038
IS - 2
SP - 101
EP - 118
AB - Two point boundary value problem for the linear system of ordinary differential equations with deviating arguments \[{{x}^{\prime }(t) ={A}(t){x}(\tau _{11}(t))+{B}(t){u}(\tau _{12}(t)) +{q}_1(t)\,, {u}^{\prime }(t) ={C}(t){x}(\tau _{21}(t))+{D}(t){u}(\tau _{22}(t)) +{q}_2(t)\,, \alpha _{11} {x}(0) + \alpha _{12} {u}(0) = {c}_0, \quad \alpha _{21} {x}(T) + \alpha _{22} {u}(T) = {c}_T} \] is considered. For this problem the sufficient condition for existence and uniqueness of solution is obtained. The same approach as in [2], [3] is applied.
LA - eng
KW - existence and uniqueness of solution; two point linear boundary value problem; linear system of ordinary differential equations; deviating argument; delay; existence; uniqueness; two-point linear boundary value problem
UR - http://eudml.org/doc/248944
ER -

References

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