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Mat. Sb., 1993, Volume 184, Number 7, Pages 79–116 (Mi msb1000)  

This article is cited in 10 scientific papers (total in 10 papers)

On global existence of an implicit function

I. G. Tsar'kov


Abstract: The problem of global existence of an implicit function is studied, i.e., the properties of Banach spaces $X$$Y$$Z$ and functions
$$ F\colon X\times Y\to Z, $$
for which a smooth solution $y=\varphi(x)$ of the equation $F(x,y) = 0$ is possible with given initial condition $y_0=\varphi(x_0)$, where $ F(x_0,y_0)=0$. It is shown that excessive smoothness of $F$ with respect to $y$ is necessary for the existence of a smooth global solution (in comparison with a local solution).

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1994, 79:2, 287–313

Bibliographic databases:

UDC: 517.275
MSC: Primary 58C15, 46G05, 26E15, 26B10; Secondary 47H17
Received: 28.01.1992

Citation: I. G. Tsar'kov, “On global existence of an implicit function”, Mat. Sb., 184:7 (1993), 79–116; Russian Acad. Sci. Sb. Math., 79:2 (1994), 287–313

Citation in format AMSBIB
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\by I.~G.~Tsar'kov
\paper On global existence of an~implicit function
\jour Mat. Sb.
\yr 1993
\vol 184
\issue 7
\pages 79--116
\mathnet{http://mi.mathnet.ru/msb1000}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1235291}
\zmath{https://zbmath.org/?q=an:0824.58010}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 79
\issue 2
\pages 287--313
\crossref{https://doi.org/10.1070/SM1994v079n02ABEH003501}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1994PY27400004}


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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. I. G. Tsar'kov, “Smoothing of abstract functions”, Russian Acad. Sci. Sb. Math., 83:2 (1995), 405–430  mathnet  crossref  mathscinet  zmath  isi
    2. I. G. Tsar'kov, “Some topics on the continuation and smoothing of vector functions”, Math. Notes, 58:6 (1995), 1327–1335  mathnet  crossref  mathscinet  zmath  isi
    3. I. G. Tsar'kov, “Right inverse operators and $\varepsilon$-selections”, Russian Math. Surveys, 50:2 (1995), 453–454  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. I. G. Tsar'kov, “On the extension and smoothing of vector-valued functions”, Izv. Math., 59:4 (1995), 847–879  mathnet  crossref  mathscinet  zmath  isi
    5. Tsarkov I., “On Smooth Selections Form Sets of Almost Chebyshev Centres”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1996, no. 2, 92–94  mathscinet  isi
    6. Tsar'kov I., “On Smooth Regularizations”, Dokl. Akad. Nauk, 358:5 (1998), 607–608  mathnet  mathscinet  zmath  isi
    7. M.V.. Balashov, Dušan Repovš, “On the splitting problem for selections”, Journal of Mathematical Analysis and Applications, 355:1 (2009), 277  crossref  mathscinet  zmath
    8. I. G. Tsar'kov, “Stability of Unique Solvability of Quasilinear Equations Given Additional Data”, Math. Notes, 90:6 (2011), 894–919  mathnet  crossref  crossref  mathscinet  isi
    9. S. S. Ajiev, “Hölder analysis and geometry on Banach spaces: homogeneous homeomorphisms and commutative group structures, approximation and Tzar’kov’s phenomenon. Part I”, Eurasian Math. J., 5:1 (2014), 7–60  mathnet
    10. S. S. Ajiev, “Hölder analysis and geometry on Banach spaces: homogeneous homeomorphisms and commutative group structures, approximation and Tzar'kov's phenomenon. Part II”, Eurasian Math. J., 5:2 (2014), 7–51  mathnet
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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