Abstract:
This paper considers multivalued mappings which map a compact metric space into the space of nonempty closed subsets of L1I. A theorem asserting the existence of a continuous branch of such a mapping is proved. This theorem is analogous to a theorem of Michael. As corollaries, theorems on the existence of fixed points of multivalued mappings and on the existence of solutions of differential inclusions are proved.
Bibliography: 13 titles.
\Bibitem{Bog83}
\by A.~V.~Bogatyrev
\paper Continuous branches of multivalued mappings with nonconvex right side
\jour Math. USSR-Sb.
\yr 1984
\vol 48
\issue 2
\pages 339--348
\mathnet{http://mi.mathnet.ru/eng/sm2134}
\crossref{https://doi.org/10.1070/SM1984v048n02ABEH002678}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=691982}
\zmath{https://zbmath.org/?q=an:0547.34013}
Linking options:
https://www.mathnet.ru/eng/sm2134
https://doi.org/10.1070/SM1984v048n02ABEH002678
https://www.mathnet.ru/eng/sm/v162/i3/p344
This publication is cited in the following 5 articles:
L. I. Danilov, “Shift dynamical systems and measurable selectors of multivalued maps”, Sb. Math., 209:11 (2018), 1611–1643
Multivalued Differential Equations, 1992, 243
A. I. Bulgakov, “Continuous branches of multivalued mappings and functional-differential inclusions with nonconvex right-hand side”, Math. USSR-Sb., 71:2 (1992), 273–287
A. I. Bulgakov, “On the question of the existence of continuous branches of multivalued mappings with nonconvex images in spaces of summable functions”, Math. USSR-Sb., 64:1 (1989), 295–303
A. A. Tolstonogov, I. A. Finogenko, “On solutions of a differential inclusion with lower semicontinuous nonconvex right-hand side in a Banach space”, Math. USSR-Sb., 53:1 (1986), 203–231
Citation in format AMSBIB
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