Orbital Euclidean Stability of the Solutions of Impulsive Equations on the Impulsive Moments
Pure and Applied Mathematics Journal
Volume 4, Issue 1, February 2015, Pages: 1-8
Received: Dec. 29, 2014; Accepted: Jan. 11, 2015; Published: Jan. 27, 2015
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Author
Katya Georgieva Dishlieva, Faculty of Applied Mathematics and Informatics, Technical University of Sofia, Sofia, Bulgaria
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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.
Keywords
Euclidean Distance, Parametric Curves, Impulsive Differential Equations Orbital Euclidean Stability
To cite this article
Katya Georgieva Dishlieva, Orbital Euclidean Stability of the Solutions of Impulsive Equations on the Impulsive Moments, Pure and Applied Mathematics Journal. Vol. 4, No. 1, 2015, pp. 1-8. doi: 10.11648/j.pamj.20150401.11
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