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

Received: 9 September 2013     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.

Published in American Journal of Applied Mathematics (Volume 1, Issue 4)
DOI 10.11648/j.ajam.20130104.13
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), 2013. Published by Science Publishing Group

Keywords

Autonomous Differential Equations, Reachable Sets

References
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[3] A. Dishliev, K. Dishlieva, "Continuous dependence of the solutions of differential equations under "short" perturbations on the right–hand side," Communications in Applied Analysis, Vol. 10, Issue 2, (2006), 149-159.
[4] A. Dishliev, K. Dishlieva, S. Nenov, Specific asymptotic properties of the solutions of impulsive differential equations. Methods and applications, Academic Publications, Ltd. (2012).
[5] K. Dishlieva, "Impulsive differential equations and applications," J. Applied & Computational Mathematics, Vol. 1, Issue 6, (2012), 1-3.
[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.
[7] A. Dishliev, K. Dishlieva, "Orbital Hausdorff continuous dependence of the solutions of impulsive differential equations with respect to impulsive perturbations," International J. of Pure and Applied Mathematics, Vol. 70, Issue 2, (2011), 167-187.
[8] S. Nenov, "Impulsive controllability and optimizations problems in population dynamics," Nonlinear Analysis, Vol. 36, Issue 7, (1999), 881-890.
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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

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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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    AU  - Sashka Petkova
    AU  - Andrey Antonov
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    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
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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
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Author Information
  • University of Chemical Technology and Metallurgy, Sofia, Bulgaria

  • University of Chemical Technology and Metallurgy, Sofia, Bulgaria

  • Technical University of Sofia, Sofia, Bulgaria

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