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 CMFD, 2003, Volume 1, Pages 121–129 (Mi cmfd34)

Almost-Normed Spaces of Functions with Given Asymptotics, Lagrangian Asymptotics, and Their Application to Ordinary Differential Equations

L. D. Kudryavtsev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The concept of almost-normed spaces is introduced. It is proved that the space of sufficiently smooth functions asymptotically approximating to polynomials (of degrees no higher than a given one) as their argument tends to infinity is an almost-normed space. It is demonstrated that this space is a complete metric space with respect to the metrics generated by the almost-norm introduced. The space of functions strongly asymptotically approximating to polynomials is defined, and its embedding into the space of functions asymptotically approximating to polynomials is proved. The results obtained give a new approach to studying boundary-value problems with asymptotic initial value data at singular points of ordinary differential equations.

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English version:
Journal of Mathematical Sciences, 2004, 124:4, 5154–5162

Bibliographic databases:

UDC: 517.51+517.926

Citation: L. D. Kudryavtsev, “Almost-Normed Spaces of Functions with Given Asymptotics, Lagrangian Asymptotics, and Their Application to Ordinary Differential Equations”, Proceedings of the International Conference on Differential and Functional-Differential Equations — Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11–17 August, 2002). Part 1, CMFD, 1, MAI, M., 2003, 121–129; Journal of Mathematical Sciences, 124:4 (2004), 5154–5162

Citation in format AMSBIB
\Bibitem{Kud03} \by L.~D.~Kudryavtsev \paper Almost-Normed Spaces of Functions with Given Asymptotics, Lagrangian Asymptotics, and Their Application to Ordinary Differential Equations \inbook Proceedings of the International Conference on Differential and Functional-Differential Equations --- Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11--17 August, 2002). Part~1 \serial CMFD \yr 2003 \vol 1 \pages 121--129 \publ MAI \publaddr M. \mathnet{http://mi.mathnet.ru/cmfd34} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2129131} \zmath{https://zbmath.org/?q=an:1078.34520} \transl \jour Journal of Mathematical Sciences \yr 2004 \vol 124 \issue 4 \pages 5154--5162 \crossref{https://doi.org/10.1023/B:JOTH.0000047250.83802.5b}