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CMFD, 2007, Volume 24, Pages 3–159 (Mi cmfd100)  

This article is cited in 7 scientific papers (total in 7 papers)

Manifold Method in Eigenvector Theory of Nonlinear Operators

Ya. M. Dymarskii

Luhansk Taras Schevchenko State Pedagogical University

Abstract: First of all, this work is devoted to studying eigenvectors of nonlinear operators of general form. It is shown that manifolds generated by a family of linear operators are naturally connected with a nonlinear operator. These manifolds are an effective tool for studying the eigenvector problem of nonlinear, as well as linear operators. The description of the properties of the manifolds is of independent interest, and a considerable part of the work is devoted to it.

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English version:
Journal of Mathematical Sciences, 2008, 154:5, 655–815

Bibliographic databases:

UDC: 517.988.57+517.984.46

Citation: Ya. M. Dymarskii, “Manifold Method in Eigenvector Theory of Nonlinear Operators”, Functional analysis, CMFD, 24, PFUR, M., 2007, 3–159; Journal of Mathematical Sciences, 154:5 (2008), 655–815

Citation in format AMSBIB
\Bibitem{Dym07}
\by Ya.~M.~Dymarskii
\paper Manifold Method in Eigenvector Theory of Nonlinear Operators
\inbook Functional analysis
\serial CMFD
\yr 2007
\vol 24
\pages 3--159
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd100}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2342532}
\zmath{https://zbmath.org/?q=an:1152.35083}
\elib{http://elibrary.ru/item.asp?id=14689527}
\transl
\jour Journal of Mathematical Sciences
\yr 2008
\vol 154
\issue 5
\pages 655--815
\crossref{https://doi.org/10.1007/s10958-008-9200-6}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-54849440310}


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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. Dymarskii Ya., Ivanova O., Masyuta E., “Local research of manifolds generated by families of self-adjoint operators”, Topology, 48:2-4 (2009), 213–223  crossref  mathscinet  zmath  isi  elib
    2. Ya. M. Dymarskii, D. N. Nepiypa, “A quasilinear method in the theory of small eigenfunctions for nonlinear periodic boundary-value problems”, Journal of Mathematical Sciences, 171:1 (2010), 58–73  mathnet  crossref  mathscinet
    3. Dymarskii Ya., Nepiypa D., “Bifurcations in the case of twofold degeneration. The quasi-linear approach”, Topol. Methods Nonlinear Anal., 38:1 (2011), 169–186  mathscinet  zmath  isi  elib
    4. Bondar A.A., Dymarskii Ya.M., “Submanifolds of compact operators with fixed multiplicities of eigenvalues”, Ukrainian Math. J., 63:9 (2012), 1349–1360  crossref  mathscinet  zmath  isi
    5. M. Yu. Kokurin, “Reduction of variational inequalities with irregular operators on a ball to regular operator equations”, Russian Math. (Iz. VUZ), 57:4 (2013), 26–34  mathnet  crossref
    6. A. A. Bondar', “On parametrization of the submanifold of matrices with a fixed structure of Jordan blocks”, Siberian Math. J., 56:6 (2015), 996–1008  mathnet  crossref  crossref  mathscinet  isi  elib
    7. Ya. M. Dymarskii, Yu. A. Evtushenko, “Foliation of the space of periodic boundary-value problems by hypersurfaces corresponding to fixed lengths of the $n$th spectral lacuna”, Sb. Math., 207:5 (2016), 678–701  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Современная математика. Фундаментальные направления
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