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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.

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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


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    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  mathnet  crossref  mathscinet  zmath
    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. L. D. Kudryavtsev, “Lagrangian asymptotic behaviour of solutions of inhomogeneous systems of ordinary differential equations”, Sb. Math., 197:9 (2006), 1341–1351  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Kudryavtsev L.D., “Problems with asymptotic initial data for systems of ordinary differential equations”, Doklady Mathematics, 73:2 (2006), 202–204  crossref  mathscinet  zmath  isi  elib  scopus
    5. Kalyakin L., “Justification of an Asymptotic Expansion at Infinity”, Journal of Nonlinear Mathematical Physics, 15, Suppl. 3 (2008), 220–226  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. L. A. Kalyakin, “Metod usredneniya v zadachakh ob asimptotike na beskonechnosti”, Ufimsk. matem. zhurn., 1:2 (2009), 29–52  mathnet  zmath  elib
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