The asymptotic behaviour of the solution to a system of differential equations with a small parameter and singular initial point

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© 2010 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.
, , Citation Arlen M Il'in et al 2010 Sb. Math. 201 79 DOI 10.1070/SM2010v201n01ABEH004066

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1 Chelyabinsk State University, Chelyabinsk, Russian Federation

2 Urals State University, Ekaterinburg, Russian Federation

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1064-5616/201/1/79

Abstract

The initial value problem for a system of nonlinear ordinary differential equations with a small parameter multiplying the highest derivative is investigated. In a neighbourhood of the initial point the asymptotic behaviour of the solution has quite a complicated structure. A uniform asymptotic approximation to the solution up to an arbitrary power of the small parameter is constructed and substantiated.

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10.1070/SM2010v201n01ABEH004066