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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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http://mi.mathnet.ru/eng/izv581https://doi.org/10.4213/im581 http://mi.mathnet.ru/eng/izv/v72/i4/p97
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N. A. Demyankov, “Variatsionnye neravenstva i printsip virtualnykh peremeschenii”, Model. i analiz inform. sistem, 17:3 (2010), 48–57
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V. S. Klimov, N. A. Demyankov, “Relative rotation and variational inequalities”, Russian Math. (Iz. VUZ), 55:6 (2011), 37–45
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N. A. Demyankov, V. S. Klimov, “Ob odnom klasse operatornykh vklyuchenii”, Model. i analiz inform. sistem, 19:3 (2012), 63–72
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V. S. Klimov, “Operator Inclusions and Quasi-Variational Inequalities”, Math. Notes, 101:5 (2017), 863–877
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