Continuous dependence of inverse fundamental matrices of generalized linear ordinary differential equations on a parameter

Zdeněk Halas

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2005)

  • Volume: 44, Issue: 1, page 39-48
  • ISSN: 0231-9721

Abstract

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The problem of continuous dependence for inverses of fundamental matrices in the case when uniform convergence is violated is presented here.

How to cite

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Halas, Zdeněk. "Continuous dependence of inverse fundamental matrices of generalized linear ordinary differential equations on a parameter." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 44.1 (2005): 39-48. <http://eudml.org/doc/32451>.

@article{Halas2005,
abstract = {The problem of continuous dependence for inverses of fundamental matrices in the case when uniform convergence is violated is presented here.},
author = {Halas, Zdeněk},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {generalized linear ordinary differential equations; fundamental matrix; adjoint equation; continuous dependence on a parameter; emphatic convergence},
language = {eng},
number = {1},
pages = {39-48},
publisher = {Palacký University Olomouc},
title = {Continuous dependence of inverse fundamental matrices of generalized linear ordinary differential equations on a parameter},
url = {http://eudml.org/doc/32451},
volume = {44},
year = {2005},
}

TY - JOUR
AU - Halas, Zdeněk
TI - Continuous dependence of inverse fundamental matrices of generalized linear ordinary differential equations on a parameter
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2005
PB - Palacký University Olomouc
VL - 44
IS - 1
SP - 39
EP - 48
AB - The problem of continuous dependence for inverses of fundamental matrices in the case when uniform convergence is violated is presented here.
LA - eng
KW - generalized linear ordinary differential equations; fundamental matrix; adjoint equation; continuous dependence on a parameter; emphatic convergence
UR - http://eudml.org/doc/32451
ER -

References

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  1. Ashordia M., On the correctness of linear boundary value problems for systems of generalized ordinary differential equations, Proceedings of the Georgian Academy of Sciences, Math. 1, 4 (1993), 385–394. (1993) Zbl0797.34015MR1262572
  2. Kurzweil J., Generalized ordinary differential equations and continuous dependence on a parameter, Czech. Math. J. 7 (82) (1957), 418–449. (1957) Zbl0090.30002MR0111875
  3. Kurzweil J., Generalized ordinary differential equations, Czech. Math. J. 24 (83) (1958), 360–387. (1958) Zbl0102.07003MR0111878
  4. Schwabik Š.: Generalized Ordinary Differential Equations., World Scientific, Singapore, , 1992. (1992) MR1200241
  5. Schwabik Š., Tvrdý M., Vejvoda O.: Differential, Integral Equations: Boundary Value Problems, Adjoints., Academia and D. Reidel, Praha and Dordrecht, , 1979. (1979) MR0542283
  6. Schwabik Š., Tvrdý M., Boundary value problems for generalized linear differential equations, Czech. Math. J. 29 (104) (1979), 451–477. (1979) MR0536070
  7. Tvrdý M., Differential and integral equations in the space of regulated functions, In: Memoirs on Differential Equations and Mathematical Physics, vol. 25, 2002, 1–104. Zbl1081.34504MR1903190
  8. Tvrdý M., Stieltjesův integrál, Učební text [online, cited 22. 6. 2005], http://www.math.cas.cz/~tvrdy/teaching.html. 

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