Generalized differential equations in the space of regulated functions (boundary value problems and controllability)

Milan Tvrdý

Mathematica Bohemica (1991)

  • Volume: 116, Issue: 3, page 225-244
  • ISSN: 0862-7959

Abstract

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Boundary value problems for generalized linear differential equations and the corresponding controllability problems are dealt with. The adjoint problems are introduced in such a way that the usual duality theorems are valid. As a special case the interface boundary value problems are included. In contrast to the earlier papers by the author the right-hand side of the generalized differential equations as well as the solutions of this equation can be in general regulated functions (not necessarily of bounded variation). Similar problems in the space of regulated functions were treated e.g. by Ch. S. Hönig, L. Fichmann and L. Barbanti, who made use of the interior (Dushnik) integral. In this paper the integral is the Perron-Stieltjes (Kurzweil) integral.

How to cite

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Tvrdý, Milan. "Generalized differential equations in the space of regulated functions (boundary value problems and controllability)." Mathematica Bohemica 116.3 (1991): 225-244. <http://eudml.org/doc/29328>.

@article{Tvrdý1991,
abstract = {Boundary value problems for generalized linear differential equations and the corresponding controllability problems are dealt with. The adjoint problems are introduced in such a way that the usual duality theorems are valid. As a special case the interface boundary value problems are included. In contrast to the earlier papers by the author the right-hand side of the generalized differential equations as well as the solutions of this equation can be in general regulated functions (not necessarily of bounded variation). Similar problems in the space of regulated functions were treated e.g. by Ch. S. Hönig, L. Fichmann and L. Barbanti, who made use of the interior (Dushnik) integral. In this paper the integral is the Perron-Stieltjes (Kurzweil) integral.},
author = {Tvrdý, Milan},
journal = {Mathematica Bohemica},
keywords = {generalized differential equations; adjoint operators; existence and uniqueness theorems; controllability; regulated function; boundary value problem; adjoint problem; interface problem; Peron-Stieltjes integral; Kurzweil integral; generalized differential equations; adjoint operators; existence and uniqueness theorems; controllability},
language = {eng},
number = {3},
pages = {225-244},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalized differential equations in the space of regulated functions (boundary value problems and controllability)},
url = {http://eudml.org/doc/29328},
volume = {116},
year = {1991},
}

TY - JOUR
AU - Tvrdý, Milan
TI - Generalized differential equations in the space of regulated functions (boundary value problems and controllability)
JO - Mathematica Bohemica
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 116
IS - 3
SP - 225
EP - 244
AB - Boundary value problems for generalized linear differential equations and the corresponding controllability problems are dealt with. The adjoint problems are introduced in such a way that the usual duality theorems are valid. As a special case the interface boundary value problems are included. In contrast to the earlier papers by the author the right-hand side of the generalized differential equations as well as the solutions of this equation can be in general regulated functions (not necessarily of bounded variation). Similar problems in the space of regulated functions were treated e.g. by Ch. S. Hönig, L. Fichmann and L. Barbanti, who made use of the interior (Dushnik) integral. In this paper the integral is the Perron-Stieltjes (Kurzweil) integral.
LA - eng
KW - generalized differential equations; adjoint operators; existence and uniqueness theorems; controllability; regulated function; boundary value problem; adjoint problem; interface problem; Peron-Stieltjes integral; Kurzweil integral; generalized differential equations; adjoint operators; existence and uniqueness theorems; controllability
UR - http://eudml.org/doc/29328
ER -

References

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