RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Guidelines for authors License agreement Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Trudy MIAN: Year: Volume: Issue: Page: Find

 Personal entry: Login: Password: Save password Enter Forgotten password? Register

 Tr. Mat. Inst. Steklova, 2001, Volume 232, Pages 194–217 (Mi tm213)

This article is cited in 5 scientific papers (total in 6 papers)

Asymptotics of Solutions to Differential Equations near Singular Points

L. D. Kudryavtsev

Abstract: Conditions are obtained under which all solutions to a normal system of equations asymptotically or strongly asymptotically approximate to polynomials as the argument tends to infinity. For the system of the form $L\mathbf x=\mathbf f$, where $L$ is a first-order linear differential operator, conditions are found under which all its solutions $L$-asymptotically approximate to the solutions of the homogeneous system $L\mathbf x=\mathbf 0$ as the argument tends to the singular point of the former system.

Full text: PDF file (282 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2001, 232, 187–210

Bibliographic databases:
UDC: 517.911
Received in August 2000

Citation: L. D. Kudryavtsev, “Asymptotics of Solutions to Differential Equations near Singular Points”, Function spaces, harmonic analysis, and differential equations, Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii, Tr. Mat. Inst. Steklova, 232, Nauka, MAIK «Nauka/Inteperiodika», M., 2001, 194–217; Proc. Steklov Inst. Math., 232 (2001), 187–210

Citation in format AMSBIB
\Bibitem{Kud01} \by L.~D.~Kudryavtsev \paper Asymptotics of Solutions to Differential Equations near Singular Points \inbook Function spaces, harmonic analysis, and differential equations \bookinfo Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii \serial Tr. Mat. Inst. Steklova \yr 2001 \vol 232 \pages 194--217 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm213} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1851449} \zmath{https://zbmath.org/?q=an:1011.34040} \transl \jour Proc. Steklov Inst. Math. \yr 2001 \vol 232 \pages 187--210 

Linking options:
• http://mi.mathnet.ru/eng/tm213
• http://mi.mathnet.ru/eng/tm/v232/p194

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. L. D. Kudryavtsev, “Almost-Normed Spaces of Functions with Given Asymptotics, Lagrangian Asymptotics, and Their Application to Ordinary Differential Equations”, Journal of Mathematical Sciences, 124:4 (2004), 5154–5162
2. A. A. Bolibrukh, V. A. Il'in, S. M. Nikol'skii, V. M. Filippov, G. N. Yakovlev, “Lev Dmitrievich Kudryavtsev (on his 80th birthday)”, Russian Math. Surveys, 60:1 (2005), 177–188
3. L. D. Kudryavtsev, “Lagrangian asymptotic behaviour of solutions of inhomogeneous systems of ordinary differential equations”, Sb. Math., 197:9 (2006), 1341–1351
4. Kudryavtsev L.D., “Problems with asymptotic initial data for systems of ordinary differential equations”, Doklady Mathematics, 73:2 (2006), 202–204
5. Kalyakin L., “Justification of an Asymptotic Expansion at Infinity”, Journal of Nonlinear Mathematical Physics, 15, Suppl. 3 (2008), 220–226
6. L. A. Kalyakin, “Metod usredneniya v zadachakh ob asimptotike na beskonechnosti”, Ufimsk. matem. zhurn., 1:2 (2009), 29–52
•  Number of views: This page: 432 Full text: 126 References: 52

 Contact us: math-net2019_12 [at] mi-ras ru Terms of Use Registration Logotypes © Steklov Mathematical Institute RAS, 2019