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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  1. On boundary value problems for systems of linear functional differential equations, Czechoslovak Math. J. 47 No. 2 (1997), 233–244. MR1452425
  2. On a Two Point Boundary Value Problem for Linear System of ODEs, in press. 
  3. On one Two Point Boundary Value Problem for Linear System of ODEs with Deviating Arguments, CDDE 2000 Program, Abstract, Extended abstracts, Masaryk University, Brno 2000, 75–76. 
  4. Inequalities: Theory of Majorization and Its Applications, Academic Press, 1979, (in Russian), Mir, Moskva, 1983. MR0731533
  5. An initial value problem and boundary value problems for systems of ordinary differential equations. Vol.I: Linear theory, MU Brno 1997 (in Czech), Macniereba, Tbilisi 1997, 216pp. (in Russian). Zbl0956.34505MR1484729
  6. On the nonlocal boundary value problem for first order loaded differential equations, Indian J. Pure Appl. Math. 26, No. 4 (1995), 309–314. MR1328759
  7. Boundary value problems and Green’s operator functions, Glas. Mat. Ser. III 24(44), No. 4 (1989), 511–522. Zbl0712.34024MR1080079
  8. An algebraic approach for solving boundary value matrix problem: Existence, uniqueness and closed form solutions, Rev. Mat. Complut. 1, No. 1-3 (1988), 145–155. MR0977046
  9. On the Vallée-Poussin problem for singular differential equations with deviating arguments, Arch. Math. (Brno) 33 No. 1-2 (1997), 127–138. MR1464307
  10. Introduction into theory of differential equations with deviating argument, Nauka Moskva 1971 (in Russian). MR0352646
  11. Spectrum control in systems with delay, Avtom. Telemekh. No. 7, (1976), 5–14 (in Russian). MR0444207
  12. Modal control of multiinput linear systems with delay, Avtom. Telemekh. No. 1 (1980), 5–10 (in Russian). 

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