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Izv. RAN. Ser. Mat., 2008, Volume 72, Issue 4, Pages 97–120 (Mi izv581)  

This article is cited in 4 scientific papers (total in 4 papers)

Topological characteristics of multi-valued maps and Lipschitzian functionals

V. S. Klimov

P. G. Demidov Yaroslavl State University

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.

DOI: https://doi.org/10.4213/im581

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English version:
Izvestiya: Mathematics, 2008, 72:4, 717–739

Bibliographic databases:

UDC: 517.946
MSC: 58C30, 55M20, 58E05, 35K55, 34G99, 34A60, 34A26, 34C11, 34A34, 47E05, 47F05
Received: 14.04.2005
Revised: 29.12.2006

Citation: V. S. Klimov, “Topological characteristics of multi-valued maps and Lipschitzian functionals”, Izv. RAN. Ser. Mat., 72:4 (2008), 97–120; Izv. Math., 72:4 (2008), 717–739

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. A. Demyankov, “Variatsionnye neravenstva i printsip virtualnykh peremeschenii”, Model. i analiz inform. sistem, 17:3 (2010), 48–57  mathnet  elib
    2. V. S. Klimov, N. A. Demyankov, “Relative rotation and variational inequalities”, Russian Math. (Iz. VUZ), 55:6 (2011), 37–45  mathnet  crossref  mathscinet  elib
    3. N. A. Demyankov, V. S. Klimov, “Ob odnom klasse operatornykh vklyuchenii”, Model. i analiz inform. sistem, 19:3 (2012), 63–72  mathnet
    4. V. S. Klimov, “Operator Inclusions and Quasi-Variational Inequalities”, Math. Notes, 101:5 (2017), 863–877  mathnet  crossref  crossref  mathscinet  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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