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Uspekhi Mat. Nauk, 1976, Volume 31, Issue 6(192), Pages 102–122 (Mi umn4011)  

This article is cited in 6 scientific papers (total in 6 papers)

The development of the theory of ordinary differential equations with a small parameter multiplying the highest derivative during the period 1966–1976

A. B. Vasil'eva


Abstract: We survey the results relating to the theory of singular perturbations, in particular, to the theory of ordinary differential equations with a small parameter multiplying the highest derivative, that have been obtained by pupils of A. N. Tikhonov during the period 1966-1976. The main attention is directed at problems in which the roots of the characteristic equation have real parts of different signs (the conditionally stable case), and also at problems in which the characteristic equation has roots that are identically zero.

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English version:
Russian Mathematical Surveys, 1976, 31:6, 109–131

Bibliographic databases:

UDC: 517.9
MSC: 34E15, 34E05, 15A18, 34Bxx, 34K10
Received: 09.07.1976

Citation: A. B. Vasil'eva, “The development of the theory of ordinary differential equations with a small parameter multiplying the highest derivative during the period 1966–1976”, Uspekhi Mat. Nauk, 31:6(192) (1976), 102–122; Russian Math. Surveys, 31:6 (1976), 109–131

Citation in format AMSBIB
\Bibitem{Vas76}
\by A.~B.~Vasil'eva
\paper The development of the theory of ordinary differential equations with a~small parameter multiplying the highest derivative during the period 1966--1976
\jour Uspekhi Mat. Nauk
\yr 1976
\vol 31
\issue 6(192)
\pages 102--122
\mathnet{http://mi.mathnet.ru/umn4011}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=473373}
\zmath{https://zbmath.org/?q=an:0366.34044|0376.34045}
\transl
\jour Russian Math. Surveys
\yr 1976
\vol 31
\issue 6
\pages 109--131
\crossref{https://doi.org/10.1070/RM1976v031n06ABEH001580}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. R. E. O’Malley, Jr, “A Singular Singularly-Perturbed Linear Boundary Value Problem”, SIAM J Math Anal, 10:4 (1979), 695  crossref  mathscinet  zmath
    2. J. J. Mahony, J. J. Shepherd, “Stiff systems of ordinary differential equations. Part 1. Completely stiff, homogeneous systems”, J Aust Math Soc Series B Appl Math, 23:1 (1981), 17  crossref  mathscinet  zmath  isi
    3. V. S. Korolyuk, “The Boundary Layer in the Asymptotic Analysis of Random Walks”, Theory Probab Appl, 34:1 (1989), 179  mathnet  crossref  mathscinet  zmath  isi
    4. “Singular Perturbations and Time Scales in Guidance and Control of Aerospace Systems: A Survey”, Journal of Guidance, Control, and Dynamics, 24:6 (2001), 1057  crossref
    5. Walter Kelley, “Perturbation problems with quadratic dependence on the first derivative”, Nonlinear Analysis: Theory, Methods & Applications, 51:3 (2002), 469  crossref
    6. D. Subbaram Naidu, “Singular perturbations and hysteresis. Michael P. Mortell, Robert E. O'Malley, Alexei Pokrovskii and Vladimir Sobolev, Society of Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2005. No. of pages: xiv+344. Price: $66.00. ISBN 0-089871-597-0”, Int J Robust Nonlinear Control, 17:12 (2007), 1155  crossref  mathscinet
  • Успехи математических наук Russian Mathematical Surveys
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