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Sibirsk. Mat. Zh., 2003, Volume 44, Number 6, Pages 1255–1265 (Mi smj1252)  

A modified regularization method

O. P. Germanovicha, A. V. Malyshevb

a North-Western State Correspondence Technical University
b Federal Network Company

Abstract: We consider the Cauchy problem for the systems of the first-order ordinary differential equations with a small parameter $E$ of degree $q$ at the derivative. We study the possibility of solving this problem by means of the regularization method of the Lomov theory of singular perturbations. We show that, for $q>1$, an application of the procedure by Lomov leads only to the trivial solution to the problem in the class of resonance-free solutions. We suggest and describe a modification of the procedure which enables us to construct a nontrivial solution to the problem in the space of resonance-free solutions.

Keywords: singularity, perturbation, regularization

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English version:
Siberian Mathematical Journal, 2003, 44:6, 981–990

Bibliographic databases:

UDC: 517.928.2
Received: 14.11.2001
Revised: 14.05.2003

Citation: O. P. Germanovich, A. V. Malyshev, “A modified regularization method”, Sibirsk. Mat. Zh., 44:6 (2003), 1255–1265; Siberian Math. J., 44:6 (2003), 981–990

Citation in format AMSBIB
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\by O.~P.~Germanovich, A.~V.~Malyshev
\paper A modified regularization method
\jour Sibirsk. Mat. Zh.
\yr 2003
\vol 44
\issue 6
\pages 1255--1265
\mathnet{http://mi.mathnet.ru/smj1252}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2034932}
\zmath{https://zbmath.org/?q=an:1049.34068}
\transl
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 6
\pages 981--990
\crossref{https://doi.org/10.1023/B:SIMJ.0000007473.40614.56}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000187464000005}


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