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JOURNALS // Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya // Archive
Izv. RAN. Ser. Mat., 2017 Volume 81, Issue 6, Pages 180–198 (Mi im8298)
This article is cited in 1 paper

High-frequency asymptotics of solutions of ODE in a Banach space

L. I. Sazonovab

a Southern Federal University, Rostov-on-Don
b South Mathematical Institute of VSC RAS

Abstract: We construct and justify high-frequency asymptotic expansions of solutions for some class of linear ODE in a Banach space. In particular, we obtain new results in the case when the averaged ODE are degenerate.

Keywords: periodic solution, differential equation, averaging, homogenization.

UDC: 517.928

MSC: 34G10, 34K33, 35B25, 35C20, 35K10, 47D06

Received: 17.09.2014
Revised: 09.09.2016

DOI: 10.4213/im8298


 English version: Izvestiya: Mathematics, 2017, 81:6, 1234–1252

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© Steklov Math. Inst. of RAS, 2025