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

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

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
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
3. A. V. Babin, “Fractional powers of a nonlinear analytic differential operator”, Math. USSR-Sb., 37:1 (1980), 9–38
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
5. Fursikov A., “Properties of Solutions of Some Control-Problems Connected with the Navier–Stokes System”, 262, no. 1, 1982, 44–48
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
7. P.M Fitzpatrick, Jacobo Pesjsachowicz, “Nonorientability of the index bundle and several-parameter bifurcation”, Journal of Functional Analysis, 98:1 (1991), 42
8. Ammar Alsaedy, Nikolai Tarkhanov, “Normally solvable nonlinear boundary value problems”, Nonlinear Analysis: Theory, Methods & Applications, 95 (2014), 468
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