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Mat. Sb. (N.S.), 1974, Volume 93(135), Number 3, Pages 422–450 (Mi msb3424)  

This article is cited in 8 scientific papers (total in 8 papers)

Finite dimensionality of the kernel and cokernel of quasilinear elliptic mappings

A. V. Babin


Abstract: In this work we investigate a certain class of nonlinear mappings of Banach spaces, namely, quasilinear elliptic mappings (q.e.m.'s). Examples of q.e.m.'s are given by mappings which correspond to nonlinear elliptic partial differential equations. For q.e.m.'s of a general form we obtain a theorem which is analogous to a known result on finite dimensionality of the kernel and cokernel of an elliptic linear operator. The results which we obtain are applied to elliptic nonlinear boundary value problems of a general form.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Sbornik, 1974, 22:3, 427–455

Bibliographic databases:

UDC: 517.42+519.56
MSC: Primary 47H15, 47F05; Secondary 47B30, 35J60
Received: 03.05.1973

Citation: A. V. Babin, “Finite dimensionality of the kernel and cokernel of quasilinear elliptic mappings”, Mat. Sb. (N.S.), 93(135):3 (1974), 422–450; Math. USSR-Sb., 22:3 (1974), 427–455

Citation in format AMSBIB
\Bibitem{Bab74}
\by A.~V.~Babin
\paper Finite dimensionality of the kernel and cokernel of quasilinear elliptic mappings
\jour Mat. Sb. (N.S.)
\yr 1974
\vol 93(135)
\issue 3
\pages 422--450
\mathnet{http://mi.mathnet.ru/msb3424}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=372914}
\zmath{https://zbmath.org/?q=an:0289.47031}
\transl
\jour Math. USSR-Sb.
\yr 1974
\vol 22
\issue 3
\pages 427--455
\crossref{https://doi.org/10.1070/SM1974v022n03ABEH001699}


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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. A. V. Babin, “On global solvability of nonlinear parabolic boundary-value problems”, Math. USSR-Sb., 26:1 (1975), 89–104  mathnet  crossref  mathscinet  zmath
    2. Yu. G. Borisovich, V. G. Zvyagin, Yu. I. Sapronov, “Non-linear Fredholm maps and the Leray–Schauder theory”, Russian Math. Surveys, 32:4 (1977), 1–54  mathnet  crossref  mathscinet  zmath
    3. A. V. Babin, “Fractional powers of a nonlinear analytic differential operator”, Math. USSR-Sb., 37:1 (1980), 9–38  mathnet  crossref  mathscinet  zmath  isi
    4. A. V. Fursikov, “Properties of solutions of some extremal problems connected with the Navier–Stokes system”, Math. USSR-Sb., 46:3 (1983), 323–351  mathnet  crossref  mathscinet  zmath
    5. Fursikov A., “Properties of Solutions of Some Control-Problems Connected with the Navier–Stokes System”, 262, no. 1, 1982, 44–48  isi
    6. A. V. Babin, M. I. Vishik, “Attractors of partial differential evolution equations and estimates of their dimension”, Russian Math. Surveys, 38:4 (1983), 151–213  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. P.M Fitzpatrick, Jacobo Pesjsachowicz, “Nonorientability of the index bundle and several-parameter bifurcation”, Journal of Functional Analysis, 98:1 (1991), 42  crossref
    8. Ammar Alsaedy, Nikolai Tarkhanov, “Normally solvable nonlinear boundary value problems”, Nonlinear Analysis: Theory, Methods & Applications, 95 (2014), 468  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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