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Sibirskii Matematicheskii Zhurnal, 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
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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.
Received: 14.11.2001
Revised: 14.05.2003
English version:
Siberian Mathematical Journal, 2003, Volume 44, Issue 6, Pages 981–990
DOI: https://doi.org/10.1023/B:SIMJ.0000007473.40614.56
Bibliographic databases:
UDC: 517.928.2
Language: Russian
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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\paper A modified regularization method
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\pages 1255--1265
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\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}
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    		Сибирский математический журнал Siberian Mathematical Journal
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