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Mat. Zametki, 1971, Volume 10, Issue 2, Pages 125–128 (Mi mz9695)  

This article is cited in 3 scientific papers (total in 3 papers)

A differential equation without a solution

V. V. Grushin

M. V. Lomonosov Moscow State University

Abstract: A direct construction is given of a function $f(x_1, x_2)\in C^\infty$, such that the equation
$$ \frac{\partial u}{\partial x_1}+ix_1^{2k-1}\frac{\partial u}{\partial x_2}=f $$
has no solution in any neighborhood of the origin; the function $f$ and all its derivatives vanish for $x_1=0$.

Full text: PDF file (488 kB)

English version:
Mathematical Notes, 1971, 10:2, 499–501

Bibliographic databases:

UDC: 517.9
Received: 02.04.1970

Citation: V. V. Grushin, “A differential equation without a solution”, Mat. Zametki, 10:2 (1971), 125–128; Math. Notes, 10:2 (1971), 499–501

Citation in format AMSBIB
\Bibitem{Gru71}
\by V.~V.~Grushin
\paper A differential equation without a solution
\jour Mat. Zametki
\yr 1971
\vol 10
\issue 2
\pages 125--128
\mathnet{http://mi.mathnet.ru/mz9695}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=285793}
\zmath{https://zbmath.org/?q=an:0223.35011}
\transl
\jour Math. Notes
\yr 1971
\vol 10
\issue 2
\pages 499--501
\crossref{https://doi.org/10.1007/BF01822870}


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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. Yu. V. Egorov, P. R. Popivanov, “Equations of principal type witgout solution”, Russian Math. Surveys, 29:2 (1974), 176–194  mathnet  crossref  mathscinet  zmath
    2. L. Nirenberg, “Lektsii o lineinykh differentsialnykh uravneniyakh s chastnymi proizvodnymi”, UMN, 30:4(184) (1975), 147–204  mathnet  mathscinet  zmath
    3. V. P. Burskii, “O differentsialnykh operatorakh i differentsialnykh uravneniyakh na tore”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 22:4 (2018), 607–619  mathnet  crossref  elib
  • Математические заметки Mathematical Notes
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