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Izv. RAN. Ser. Mat., 1998, Volume 62, Issue 5, Pages 117–134 (Mi izv212)  

This article is cited in 12 scientific papers (total in 12 papers)

Topological characteristics of non-smooth functionals

V. S. Klimov

Orel State University

Abstract: We establish infinite-dimensional variants of the Poincare–Hopf theorem for many-valued vector fields generated by operators of monotonic type. We suggest conditions for the stabilization of the homology groups of closed subsets of a Banach space when approximated by finite-dimensional sections. Emphasis is given to the study of topological characteristics of Lebesgue sets of Lipschitz functionals defined on a closed convex subset of a reflexive space.

DOI: https://doi.org/10.4213/im212

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English version:
Izvestiya: Mathematics, 1998, 62:5, 969–984

Bibliographic databases:

MSC: 58C30, 55M20, 58E05
Received: 03.12.1996

Citation: V. S. Klimov, “Topological characteristics of non-smooth functionals”, Izv. RAN. Ser. Mat., 62:5 (1998), 117–134; Izv. Math., 62:5 (1998), 969–984

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, “Bounded solutions of differential inclusions with homogeneous principal parts”, Izv. Math., 64:4 (2000), 755–776  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. V. S. Klimov, “Infinite-dimensional version of the Poincare–Hopf theorem and homological characteristics of functionals”, Sb. Math., 192:1 (2001), 49–64  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. V. S. Klimov, “The averaging method in the problem of periodic solutions of quasilinear parabolic equations”, Russian Math. (Iz. VUZ), 45:10 (2001), 36–43  mathnet  mathscinet  zmath  elib
    4. 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
    5. V. S. Klimov, “Type Numbers of Critical Points for Nonsmooth Functionals”, Math. Notes, 72:5 (2002), 641–651  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. V. S. Klimov, “Monotone mappings and flows of viscous media”, Siberian Math. J., 45:6 (2004), 1063–1074  mathnet  crossref  mathscinet  zmath  isi
    7. V. S. Klimov, “Deformations of Functionals and Bifurcations of Extremals”, Math. Notes, 81:1 (2007), 61–71  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    8. 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
    9. V. S. Klimov, N. A. Demyankov, “Relative rotation and variational inequalities”, Russian Math. (Iz. VUZ), 55:6 (2011), 37–45  mathnet  crossref  mathscinet  elib
    10. N. A. Demyankov, “O dvukh konechnomernykh approksimatsiyakh periodicheskoi kraevoi zadachi”, Model. i analiz inform. sistem, 18:3 (2011), 63–74  mathnet
    11. Klimov V.S., Demyankov N.A., “Diskretnye priblizheniya i periodicheskie resheniya differentsialnykh vklyuchenii”, Differentsialnye uravneniya, 49:2 (2013), 234–234  zmath  elib
    12. V. S. Klimov, “Variational inequalities with strong nonlinearities”, Russian Math. (Iz. VUZ), 58:9 (2014), 22–35  mathnet  crossref
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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