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 Sibirsk. Mat. Zh.: Year: Volume: Issue: Page: Find

 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
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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