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Matematicheskie Zametki, 1974, Volume 15, Issue 3, Pages 467–477 (Mi mzm7368)  

This article is cited in 13 scientific papers (total in 13 papers)

Peano's theorem in an infinite-dimensional Hilbert space is false even in a weakened formulation

A. N. Godunov

M. V. Lomonosov Moscow State University
Abstract: We formulate a continuous function $F\colon R\times H\to H$, where $H$ is a separable Hilbert space such that the Cauchy problem
$$ x'(t)=F(t,x(t)),\quad x(t_0)=x_0 $$
has no solution in any neighborhood of the point $t_0$, no matter what $t_0\in R$ and $x_0\in H$ are considered.
Received: 13.04.1973
English version:
Mathematical Notes, 1974, Volume 15, Issue 3, Pages 273–279
DOI: https://doi.org/10.1007/BF01438383
Bibliographic databases:
UDC: 513.88
Language: Russian
Citation: A. N. Godunov, “Peano's theorem in an infinite-dimensional Hilbert space is false even in a weakened formulation”, Mat. Zametki, 15:3 (1974), 467–477; Math. Notes, 15:3 (1974), 273–279
Citation in format AMSBIB
\Bibitem{God74}
\by A.~N.~Godunov
\paper Peano's theorem in an infinite-dimensional Hilbert space is false even in a~weakened formulation
\jour Mat. Zametki
\yr 1974
\vol 15
\issue 3
\pages 467--477
\mathnet{http://mi.mathnet.ru/mzm7368}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=352640}
\zmath{https://zbmath.org/?q=an:0297.34056|0286.34095}
\transl
\jour Math. Notes
\yr 1974
\vol 15
\issue 3
\pages 273--279
\crossref{https://doi.org/10.1007/BF01438383}
Linking options:
  • https://www.mathnet.ru/eng/mzm7368
  • https://www.mathnet.ru/eng/mzm/v15/i3/p467
  • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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