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Izv. RAN. Ser. Mat., 1992, Volume 56, Issue 6, Pages 1217–1243 (Mi izv904)  

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

Picard's theorem for ordinary differential equations in locally convex spaces

S. G. Lobanov

Moscow State Automobile and Road Technical University

Abstract: A class of infinite-dimensional Frechet spaces is constructed, including certain subspaces of $C^\infty[-1,1]$, in which Picard's theorem on solvability of an ODE with smooth right-hand side is valid in the usual formulation. Every continuous linear operator on these spaces has an exponential.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1993, 41:3, 465–487

Bibliographic databases:

UDC: 517.9
MSC: Primary 34A12, 34G20; Secondary 46A04, 46A08
Received: 23.10.1991

Citation: S. G. Lobanov, “Picard's theorem for ordinary differential equations in locally convex spaces”, Izv. RAN. Ser. Mat., 56:6 (1992), 1217–1243; Russian Acad. Sci. Izv. Math., 41:3 (1993), 465–487

Citation in format AMSBIB
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\pages 1217--1243
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\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1993
\vol 41
\issue 3
\pages 465--487
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. G. Lobanov, O. G. Smolyanov, “Ordinary differential equations in locally convex spaces”, Russian Math. Surveys, 49:3 (1994), 97–175  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Bogachev V., “Deterministic and Stochastic Differential-Equations in Infinite-Dimensional Spaces”, Acta Appl. Math., 40:1 (1995), 25–93  crossref  mathscinet  zmath  isi
    3. S. A. SHKARIN, “ON THE SOLVABILITY OF HAMILTON'S EQUATIONS IN HILBERT SPACES”, Infin. Dimens. Anal. Quantum. Probab. Relat. Top, 06:01 (2003), 145  crossref
    4. Shkarin S.A., “Compact Perturbations of Linear Differential Equations in Locally Convex Spaces”, Studia Math., 172:3 (2006), 203–227  crossref  mathscinet  zmath  isi
    5. S. G. Lobanov, “Picard's theorem for ordinary differential equations in Fréchet spaces”, Russian Math. Surveys, 62:2 (2007), 388–389  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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