Reachable Sets for Autonomous Systems of Differential Equations and their Topological Properties

Sashka Petkova; Andrey Antonov; Rumyana Chukleva

doi:doi:10.11648/j.ajam.20130104.13

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Reachable Sets for Autonomous Systems of Differential Equations and their Topological Properties

Sashka Petkova, Andrey Antonov, Rumyana Chukleva

Received: 9 September 2013 Accepted: Published: 30 October 2013

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Abstract

The initial value problems for autonomous systems of differential equations are the main object of this paper. Different variants of the concept reachable sets for the solutions of such systems are introduced. Several conditions for their existence are found and some properties are studied.

DOI	10.11648/j.ajam.20130104.13
Published in	American Journal of Applied Mathematics (Volume 1, Issue 4, October 2013)
Page(s)	49-54
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Autonomous Differential Equations, Reachable Sets

References

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[6]	K. Dishlieva, A. Dishliev, "Limitations of the solutions of differential equations with variable structure and impulses using sequences of Lyapunov functions," J. of Advanced Research in Applied Mathematics, Vol. 5, Issue 2, (2013), 39-52.
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Sashka Petkova, Andrey Antonov, Rumyana Chukleva. (2013). Reachable Sets for Autonomous Systems of Differential Equations and their Topological Properties. American Journal of Applied Mathematics, 1(4), 49-54. https://doi.org/10.11648/j.ajam.20130104.13

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ACS Style

Sashka Petkova; Andrey Antonov; Rumyana Chukleva. Reachable Sets for Autonomous Systems of Differential Equations and their Topological Properties. Am. J. Appl. Math. 2013, 1(4), 49-54. doi: 10.11648/j.ajam.20130104.13

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AMA Style

Sashka Petkova, Andrey Antonov, Rumyana Chukleva. Reachable Sets for Autonomous Systems of Differential Equations and their Topological Properties. Am J Appl Math. 2013;1(4):49-54. doi: 10.11648/j.ajam.20130104.13

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@article{10.11648/j.ajam.20130104.13,
  author = {Sashka Petkova and Andrey Antonov and Rumyana Chukleva},
  title = {Reachable Sets for Autonomous Systems of Differential Equations and their Topological Properties},
  journal = {American Journal of Applied Mathematics},
  volume = {1},
  number = {4},
  pages = {49-54},
  doi = {10.11648/j.ajam.20130104.13},
  url = {https://doi.org/10.11648/j.ajam.20130104.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20130104.13},
  abstract = {The initial value problems for autonomous systems of differential equations are the main object of this paper. Different variants of the concept reachable sets for the solutions of such systems are introduced. Several conditions for their existence are found and some properties are studied.},
 year = {2013}
}

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TY  - JOUR
T1  - Reachable Sets for Autonomous Systems of Differential Equations and their Topological Properties
AU  - Sashka Petkova
AU  - Andrey Antonov
AU  - Rumyana Chukleva
Y1  - 2013/10/30
PY  - 2013
N1  - https://doi.org/10.11648/j.ajam.20130104.13
DO  - 10.11648/j.ajam.20130104.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 49
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PB  - Science Publishing Group
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AB  - The initial value problems for autonomous systems of differential equations are the main object of this paper. Different variants of the concept reachable sets for the solutions of such systems are introduced. Several conditions for their existence are found and some properties are studied.
VL  - 1
IS  - 4
ER  -

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Author Information

Sashka Petkova

University of Chemical Technology and Metallurgy, Sofia, Bulgaria
Andrey Antonov

University of Chemical Technology and Metallurgy, Sofia, Bulgaria
Rumyana Chukleva

Technical University of Sofia, Sofia, Bulgaria

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APA Style

Sashka Petkova, Andrey Antonov, Rumyana Chukleva. (2013). Reachable Sets for Autonomous Systems of Differential Equations and their Topological Properties. American Journal of Applied Mathematics, 1(4), 49-54. https://doi.org/10.11648/j.ajam.20130104.13

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ACS Style

Sashka Petkova; Andrey Antonov; Rumyana Chukleva. Reachable Sets for Autonomous Systems of Differential Equations and their Topological Properties. Am. J. Appl. Math. 2013, 1(4), 49-54. doi: 10.11648/j.ajam.20130104.13

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AMA Style

Sashka Petkova, Andrey Antonov, Rumyana Chukleva. Reachable Sets for Autonomous Systems of Differential Equations and their Topological Properties. Am J Appl Math. 2013;1(4):49-54. doi: 10.11648/j.ajam.20130104.13

Copy | Download

@article{10.11648/j.ajam.20130104.13,
  author = {Sashka Petkova and Andrey Antonov and Rumyana Chukleva},
  title = {Reachable Sets for Autonomous Systems of Differential Equations and their Topological Properties},
  journal = {American Journal of Applied Mathematics},
  volume = {1},
  number = {4},
  pages = {49-54},
  doi = {10.11648/j.ajam.20130104.13},
  url = {https://doi.org/10.11648/j.ajam.20130104.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20130104.13},
  abstract = {The initial value problems for autonomous systems of differential equations are the main object of this paper. Different variants of the concept reachable sets for the solutions of such systems are introduced. Several conditions for their existence are found and some properties are studied.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Reachable Sets for Autonomous Systems of Differential Equations and their Topological Properties
AU  - Sashka Petkova
AU  - Andrey Antonov
AU  - Rumyana Chukleva
Y1  - 2013/10/30
PY  - 2013
N1  - https://doi.org/10.11648/j.ajam.20130104.13
DO  - 10.11648/j.ajam.20130104.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 49
EP  - 54
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20130104.13
AB  - The initial value problems for autonomous systems of differential equations are the main object of this paper. Different variants of the concept reachable sets for the solutions of such systems are introduced. Several conditions for their existence are found and some properties are studied.
VL  - 1
IS  - 4
ER  -

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