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

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

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
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
3. S. A. Lomov, A. G. Eliseev, “Asymptotic integration of singularly perturbed problems”, Russian Math. Surveys, 43:3 (1988), 1–63
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