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Izvestiya: Mathematics, 2008, Volume 72, Issue 4, Pages 717–739
DOI: https://doi.org/10.1070/IM2008v072n04ABEH002413
(Mi im581)
 

This article is cited in 5 scientific papers (total in 5 papers)

Topological characteristics of multi-valued maps and Lipschitzian functionals

V. S. Klimov

P. G. Demidov Yaroslavl State University
References:
Abstract: This paper deals with the operator inclusion $0\in F(x)+N_Q(x)$, where $F$ is a multi-valued map of monotonic type from a reflexive space $V$ to its conjugate $V^*$ and $N_Q$ is the cone normal to the closed set $Q$, which, generally speaking, is not convex. To estimate the number of solutions of this inclusion we introduce topological characteristics of multi-valued maps and Lipschitzian functionals that have the properties of additivity and homotopy invariance. We prove some infinite-dimensional versions of the Poincaré–Hopf theorem.
Received: 14.04.2005
Revised: 29.12.2006
Bibliographic databases:
UDC: 517.946
Language: English
Original paper language: Russian
Citation: V. S. Klimov, “Topological characteristics of multi-valued maps and Lipschitzian functionals”, Izv. Math., 72:4 (2008), 717–739
Citation in format AMSBIB
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\by V.~S.~Klimov
\paper Topological characteristics of multi-valued maps and Lipschitzian functionals
\jour Izv. Math.
\yr 2008
\vol 72
\issue 4
\pages 717--739
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Linking options:
  • https://www.mathnet.ru/eng/im581
  • https://doi.org/10.1070/IM2008v072n04ABEH002413
  • https://www.mathnet.ru/eng/im/v72/i4/p97
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:599
    Russian version PDF:217
    English version PDF:17
    References:93
    First page:11
     
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