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Izv. Akad. Nauk SSSR Ser. Mat., 1972, Volume 36, Issue 3, Pages 635–651 (Mi izv2316)  

This article is cited in 3 scientific papers (total in 3 papers)

The method of perturbations for singular problems

S. A. Lomov


Abstract: In this paper the regularization of a singularity with respect to a parameter is derived by means of an extension of the original operator and subsequent application of perturbation theory in an unbounded space, and used to solve an “extended” problem asymptotically. It is proved that this asymptotic solution is unique. An appropriate restriction of the asymptotic solution thus obtained will be an asymptotic solution of the original problem; this restriction is also unique. The theory of this method is illustrated by an example of an ordinary linear system of general form.

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English version:
Mathematics of the USSR-Izvestiya, 1972, 6:3, 631–648

Bibliographic databases:

UDC: 517.9
MSC: Primary 34E15; Secondary 35B25
Received: 12.02.1971

Citation: S. A. Lomov, “The method of perturbations for singular problems”, Izv. Akad. Nauk SSSR Ser. Mat., 36:3 (1972), 635–651; Math. USSR-Izv., 6:3 (1972), 631–648

Citation in format AMSBIB
\Bibitem{Lom72}
\by S.~A.~Lomov
\paper The method of perturbations for singular problems
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1972
\vol 36
\issue 3
\pages 635--651
\mathnet{http://mi.mathnet.ru/izv2316}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=330677}
\zmath{https://zbmath.org/?q=an:0273.34038}
\transl
\jour Math. USSR-Izv.
\yr 1972
\vol 6
\issue 3
\pages 631--648
\crossref{https://doi.org/10.1070/IM1972v006n03ABEH001893}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. F. Safonov, “The regularization method for singularly perturbed systems of nonlinear differential equations”, Math. USSR-Izv., 14:3 (1980), 571–596  mathnet  crossref  mathscinet  zmath  isi
    2. S. A. Lomov, A. S. Yudina, “The structure of a fundamental system of solutions of a singularly perturbed equation with a regular singular point”, Math. USSR-Izv., 21:2 (1983), 415–424  mathnet  crossref  mathscinet  zmath
    3. S. A. Lomov, A. G. Eliseev, “Asymptotic integration of singularly perturbed problems”, Russian Math. Surveys, 43:3 (1988), 1–63  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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