Pure and Applied Mathematics Journal

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Orbital Euclidean Stability of the Solutions of Impulsive Equations on the Impulsive Moments

Received: 29 December 2014    Accepted: 11 January 2015    Published: 27 January 2015
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Abstract

Curves given in a parametric form are studied in this paper. Curves are continuous on the left in the general case. Their corresponding parameters belong to the definitional intervals which is possible to not coincide for the different curves. Moreover, the points of discontinuity (if they exist) are first kind (jump discontinuity) and they are specific for each curve. Upper estimates of the Euclidean distance between two such curves are found. The results obtained are used in studies of the solutions of impulsive differential equations. Sufficient conditions for the orbital Euclidean stability of the solutions of such equations in respect to the impulsive effects on the initial condition and impulive moments are found. This type of stability is introduced and studied here for the first time.

DOI 10.11648/j.pamj.20150401.11
Published in Pure and Applied Mathematics Journal (Volume 4, Issue 1, February 2015)
Page(s) 1-8
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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

Euclidean Distance, Parametric Curves, Impulsive Differential Equations Orbital Euclidean Stability

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Author Information
  • Faculty of Applied Mathematics and Informatics, Technical University of Sofia, Sofia, Bulgaria

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    Katya Georgieva Dishlieva. (2015). Orbital Euclidean Stability of the Solutions of Impulsive Equations on the Impulsive Moments. Pure and Applied Mathematics Journal, 4(1), 1-8. https://doi.org/10.11648/j.pamj.20150401.11

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    Katya Georgieva Dishlieva. Orbital Euclidean Stability of the Solutions of Impulsive Equations on the Impulsive Moments. Pure Appl. Math. J. 2015, 4(1), 1-8. doi: 10.11648/j.pamj.20150401.11

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    AMA Style

    Katya Georgieva Dishlieva. Orbital Euclidean Stability of the Solutions of Impulsive Equations on the Impulsive Moments. Pure Appl Math J. 2015;4(1):1-8. doi: 10.11648/j.pamj.20150401.11

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  • @article{10.11648/j.pamj.20150401.11,
      author = {Katya Georgieva Dishlieva},
      title = {Orbital Euclidean Stability of the Solutions of Impulsive Equations on the Impulsive Moments},
      journal = {Pure and Applied Mathematics Journal},
      volume = {4},
      number = {1},
      pages = {1-8},
      doi = {10.11648/j.pamj.20150401.11},
      url = {https://doi.org/10.11648/j.pamj.20150401.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.pamj.20150401.11},
      abstract = {Curves given in a parametric form are studied in this paper. Curves are continuous on the left in the general case. Their corresponding parameters belong to the definitional intervals which is possible to not coincide for the different curves. Moreover, the points of discontinuity (if they exist) are first kind (jump discontinuity) and they are specific for each curve. Upper estimates of the Euclidean distance between two such curves are found. The results obtained are used in studies of the solutions of impulsive differential equations. Sufficient conditions for the orbital Euclidean stability of the solutions of such equations in respect to the impulsive effects on the initial condition and impulive moments are found. This type of stability is introduced and studied here for the first time.},
     year = {2015}
    }
    

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    AB  - Curves given in a parametric form are studied in this paper. Curves are continuous on the left in the general case. Their corresponding parameters belong to the definitional intervals which is possible to not coincide for the different curves. Moreover, the points of discontinuity (if they exist) are first kind (jump discontinuity) and they are specific for each curve. Upper estimates of the Euclidean distance between two such curves are found. The results obtained are used in studies of the solutions of impulsive differential equations. Sufficient conditions for the orbital Euclidean stability of the solutions of such equations in respect to the impulsive effects on the initial condition and impulive moments are found. This type of stability is introduced and studied here for the first time.
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