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Mat. Sb., 2001, Volume 192, Number 1, Pages 51–66 (Mi msb535)  

This article is cited in 6 scientific papers (total in 6 papers)

Infinite-dimensional version of the Poincare–Hopf theorem and homological characteristics of functionals

V. S. Klimov

P. G. Demidov Yaroslavl State University

Abstract: A version of the Poincare–Hopf theorem is established for multivalued vector fields on submanifolds of a reflexive space. The connection between the critical values and homological characteristics of the Lebesgue sets of Lipschitz functionals is studied. Applications to the theory of operator inclusions with parameters are indicated.

DOI: https://doi.org/10.4213/sm535

Full text: PDF file (305 kB)
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English version:
Sbornik: Mathematics, 2001, 192:1, 49–64

Bibliographic databases:

UDC: 517.946
MSC: Primary 58B05, 57R25; Secondary 47J25
Received: 08.12.1999

Citation: V. S. Klimov, “Infinite-dimensional version of the Poincare–Hopf theorem and homological characteristics of functionals”, Mat. Sb., 192:1 (2001), 51–66; Sb. Math., 192:1 (2001), 49–64

Citation in format AMSBIB
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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. V. S. Klimov, “Infinite-dimensional version of Morse theory for Lipschitz functionals”, Sb. Math., 193:6 (2002), 889–906  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. V. S. Klimov, “On the convergence of the conditional gradient method”, Russian Math. (Iz. VUZ), 49:12 (2005), 25–32  mathnet  mathscinet  elib
    3. V. S. Klimov, “Topological characteristics of multi-valued maps and Lipschitzian functionals”, Izv. Math., 72:4 (2008), 717–739  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. N. A. Demyankov, “Variatsionnye neravenstva i printsip virtualnykh peremeschenii”, Model. i analiz inform. sistem, 17:3 (2010), 48–57  mathnet  elib
    5. V. S. Klimov, N. A. Demyankov, “Relative rotation and variational inequalities”, Russian Math. (Iz. VUZ), 55:6 (2011), 37–45  mathnet  crossref  mathscinet  elib
    6. V. S. Klimov, “A relative variant of the Morse theory”, Russian Math. (Iz. VUZ), 57:1 (2013), 17–25  mathnet  crossref
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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