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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
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
Citation:
V. S. Klimov, “Topological characteristics of multi-valued maps and Lipschitzian functionals”, Izv. Math., 72:4 (2008), 717–739
Linking options:
https://www.mathnet.ru/eng/im581https://doi.org/10.1070/IM2008v072n04ABEH002413 https://www.mathnet.ru/eng/im/v72/i4/p97
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Abstract page: | 599 | Russian version PDF: | 217 | English version PDF: | 17 | References: | 93 | First page: | 11 |
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