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

Katya Georgieva Dishlieva

doi:doi:10.11648/j.pamj.20150401.11

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

Katya Georgieva Dishlieva

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 1)

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.

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

Keywords

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

References

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APA Style

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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ACS 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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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://article.sciencepublishinggroup.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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TY  - JOUR
T1  - Orbital Euclidean Stability of the Solutions of Impulsive Equations on the Impulsive Moments
AU  - Katya Georgieva Dishlieva
Y1  - 2015/01/27
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150401.11
DO  - 10.11648/j.pamj.20150401.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 1
EP  - 8
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150401.11
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.
VL  - 4
IS  - 1
ER  -

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Author Information

Katya Georgieva Dishlieva

Faculty of Applied Mathematics and Informatics, Technical University of Sofia, Sofia, Bulgaria

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APA Style

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

Copy | Download

ACS 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

Copy | Download

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

Copy | Download

@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://article.sciencepublishinggroup.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}
}

Copy | Download

TY  - JOUR
T1  - Orbital Euclidean Stability of the Solutions of Impulsive Equations on the Impulsive Moments
AU  - Katya Georgieva Dishlieva
Y1  - 2015/01/27
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150401.11
DO  - 10.11648/j.pamj.20150401.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 1
EP  - 8
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150401.11
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.
VL  - 4
IS  - 1
ER  -

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