Uniform Asymptotic Solutions of the Cauchy Problem for a Generalized Model Equation of L.S.Pontryagin in the Case of Violation of Conditions of Asymptotic Stability

Dilmurat Tursunov

doi:doi:10.11648/j.sjams.20130103.11

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Uniform Asymptotic Solutions of the Cauchy Problem for a Generalized Model Equation of L.S.Pontryagin in the Case of Violation of Conditions of Asymptotic Stability

Dilmurat Tursunov

Published in Science Journal of Applied Mathematics and Statistics (Volume 1, Issue 3)

Received: 18 July 2013 Published: 20 August 2013

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Abstract

Here, we construct a uniform asymptotic solution of the Cauchy problem of the small parameter for the inhomogeneous differential equation with small parameter at the derivative, when the linear part of the equation is a pure complex, with its real part changes from negative to positive when one going from the left half to the right half plane.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 1, Issue 3)
DOI	10.11648/j.sjams.20130103.11
Page(s)	25-29
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

Uniform Asymptotic Solution, the Cauchy Problem, the Small Parameter, Inhomogeneous Differential Equation, Model Equation of L. S. Pontryagin

References

[1]	Shishkova M.A. Consideration of a system of differential equations with a small parameter in the highest derivatives // DAN AN SSSR, 1973. – V. 209. – № 3. – PP.576-579.
[2]	Neishtadt A.I. Spanning the loss of stability for dynamic bifurcations. Dif.eq. 1987, v. 23, 12, -PP.2060-2067
[3]	Alymkulov K. Extension of boundary layer function method for singularly perturbed differential equation of Prandtle - Tichonov and Lighthill types // Reports of the third congress of the world mathematical society of Turkic countries, Almaty, June July, 2009, -PP 256-259.

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Dilmurat Tursunov. (2013). Uniform Asymptotic Solutions of the Cauchy Problem for a Generalized Model Equation of L.S.Pontryagin in the Case of Violation of Conditions of Asymptotic Stability. Science Journal of Applied Mathematics and Statistics, 1(3), 25-29. https://doi.org/10.11648/j.sjams.20130103.11

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ACS Style

Dilmurat Tursunov. Uniform Asymptotic Solutions of the Cauchy Problem for a Generalized Model Equation of L.S.Pontryagin in the Case of Violation of Conditions of Asymptotic Stability. Sci. J. Appl. Math. Stat. 2013, 1(3), 25-29. doi: 10.11648/j.sjams.20130103.11

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Dilmurat Tursunov. Uniform Asymptotic Solutions of the Cauchy Problem for a Generalized Model Equation of L.S.Pontryagin in the Case of Violation of Conditions of Asymptotic Stability. Sci J Appl Math Stat. 2013;1(3):25-29. doi: 10.11648/j.sjams.20130103.11

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@article{10.11648/j.sjams.20130103.11,
  author = {Dilmurat Tursunov},
  title = {Uniform Asymptotic Solutions of the Cauchy Problem for a Generalized Model Equation of L.S.Pontryagin in the Case of Violation of Conditions of Asymptotic Stability},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {1},
  number = {3},
  pages = {25-29},
  doi = {10.11648/j.sjams.20130103.11},
  url = {https://doi.org/10.11648/j.sjams.20130103.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20130103.11},
  abstract = {Here, we construct a uniform asymptotic solution of the Cauchy problem of the small parameter for the inhomogeneous differential equation with small parameter at the derivative, when the linear part of the equation is a pure complex, with its real part changes from negative to positive when one going from the left half to  the right half  plane.},
 year = {2013}
}

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TY  - JOUR
T1  - Uniform Asymptotic Solutions of the Cauchy Problem for a Generalized Model Equation of L.S.Pontryagin in the Case of Violation of Conditions of Asymptotic Stability
AU  - Dilmurat Tursunov
Y1  - 2013/08/20
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DO  - 10.11648/j.sjams.20130103.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 25
EP  - 29
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20130103.11
AB  - Here, we construct a uniform asymptotic solution of the Cauchy problem of the small parameter for the inhomogeneous differential equation with small parameter at the derivative, when the linear part of the equation is a pure complex, with its real part changes from negative to positive when one going from the left half to  the right half  plane.
VL  - 1
IS  - 3
ER  -

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Author Information

Dilmurat Tursunov

Department of Algebra and Geometry, Faculty of Mathematics and Information Technology, Osh State University, Osh City, Country Kyrgyzstan

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Dilmurat Tursunov. (2013). Uniform Asymptotic Solutions of the Cauchy Problem for a Generalized Model Equation of L.S.Pontryagin in the Case of Violation of Conditions of Asymptotic Stability. Science Journal of Applied Mathematics and Statistics, 1(3), 25-29. https://doi.org/10.11648/j.sjams.20130103.11

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ACS Style

Dilmurat Tursunov. Uniform Asymptotic Solutions of the Cauchy Problem for a Generalized Model Equation of L.S.Pontryagin in the Case of Violation of Conditions of Asymptotic Stability. Sci. J. Appl. Math. Stat. 2013, 1(3), 25-29. doi: 10.11648/j.sjams.20130103.11

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AMA Style

Dilmurat Tursunov. Uniform Asymptotic Solutions of the Cauchy Problem for a Generalized Model Equation of L.S.Pontryagin in the Case of Violation of Conditions of Asymptotic Stability. Sci J Appl Math Stat. 2013;1(3):25-29. doi: 10.11648/j.sjams.20130103.11

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@article{10.11648/j.sjams.20130103.11,
  author = {Dilmurat Tursunov},
  title = {Uniform Asymptotic Solutions of the Cauchy Problem for a Generalized Model Equation of L.S.Pontryagin in the Case of Violation of Conditions of Asymptotic Stability},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {1},
  number = {3},
  pages = {25-29},
  doi = {10.11648/j.sjams.20130103.11},
  url = {https://doi.org/10.11648/j.sjams.20130103.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20130103.11},
  abstract = {Here, we construct a uniform asymptotic solution of the Cauchy problem of the small parameter for the inhomogeneous differential equation with small parameter at the derivative, when the linear part of the equation is a pure complex, with its real part changes from negative to positive when one going from the left half to  the right half  plane.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Uniform Asymptotic Solutions of the Cauchy Problem for a Generalized Model Equation of L.S.Pontryagin in the Case of Violation of Conditions of Asymptotic Stability
AU  - Dilmurat Tursunov
Y1  - 2013/08/20
PY  - 2013
N1  - https://doi.org/10.11648/j.sjams.20130103.11
DO  - 10.11648/j.sjams.20130103.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 25
EP  - 29
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20130103.11
AB  - Here, we construct a uniform asymptotic solution of the Cauchy problem of the small parameter for the inhomogeneous differential equation with small parameter at the derivative, when the linear part of the equation is a pure complex, with its real part changes from negative to positive when one going from the left half to  the right half  plane.
VL  - 1
IS  - 3
ER  -

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