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

Mathematica Bohemica (1991)

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

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topTvrdý, 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 -

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## Citations in EuDML Documents

top- Irena Rachůnková, Milan Tvrdý, Localization of nonsmooth lower and upper functions for periodic boundary value problems
- Jan Ligęza, On two-points boundary value problems for ordinary nonlinear differential equations of the fourth order in the Colombeau algebra
- Martin Pelant, Milan Tvrdý, Linear distributional differential equations in the space of regulated functions
- Milan Tvrdý, Linear distributional differential equations of the second order

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