Variational Inequalities and Analogs of the Hopf Theorems
Matematičeskie zametki, Tome 108 (2020) no. 1, pp. 64-80.

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Properties of the approximate rotation of vector fields generated by multivalued maps of monotone type are studied. Analogs of the Hopf theorems on the extension of multivalued maps without singular points and homotopy classification of the corresponding vector fields are proved. Applications to variational inequalities and operator inclusions are outlines.
Keywords: variational inequality, operator inclusion, relative degree, multivalued map, convex set.
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V. S. Klimov. Variational Inequalities and Analogs of the Hopf Theorems. Matematičeskie zametki, Tome 108 (2020) no. 1, pp. 64-80. http://geodesic.mathdoc.fr/item/MZM_2020_108_1_a4/

[1] M. A. Krasnoselskii, P. P. Zabreiko, Geometricheskie metody nelineinogo analiza, Nelineinyi analiz i ego prilozheniya, Nauka, M., 1975 | MR | Zbl

[2] A. V. Guminskaya, P. P. Zabreiko, “O teoremakh Khopfa dlya otnositelnogo vrascheniya”, Tr. In-ta matem., 15:1 (2007), 33–46

[3] Yu. G. Borisovich, “Ob odnom primenenii ponyatiya vrascheniya vektornogo polya”, Dokl. AN SSSR, 153:1 (1963), 12–15 | MR | Zbl

[4] Yu. G. Borisovich, “Ob otnositelnom vraschenii kompaktnykh vektornykh polei v lineinykh prostranstvakh”, Tr. sem. po funkts. analizu, 1969, no. 12, 3–27 | Zbl

[5] Yu. G. Borisovich, B. D. Gelman, A. D. Myshkis, V. V. Obukhovskii, “Topologicheskie metody v teorii nepodvizhnykh tochek mnogoznachnykh otobrazhenii”, UMN, 35:1 (211) (1980), 59–126 | MR | Zbl

[6] V. S. Klimov, “O topologicheskikh kharakteristikakh negladkikh funktsionalov”, Izv. RAN. Ser. matem., 62:5 (1998), 117–134 | DOI | MR | Zbl

[7] V. S. Klimov, N. A. Demyankov, “Otnositelnoe vraschenie i variatsionnye neravenstva”, Izv. vuzov. Matem., 2011, no. 6, 44–54 | MR | Zbl

[8] I. Benedetti, V. Obukhovskii, “On the index of solvability for variational inequalities”, Set-Valued Anal., 16:1 (2008), 67–92 | DOI | MR | Zbl

[9] I. V. Skrypnik, Metody issledovaniya nelineinykh ellipticheskikh granichnykh zadach, Nauka, M., 1990 | MR | Zbl

[10] F. E. Browder, “Nonlinear elliptic boundary value problems and the generalized topological degree”, Bull. Amer. Math. Soc., 76:5 (1970), 999–1005 | DOI | MR | Zbl

[11] N. A. Bobylev, S. V. Emelyanov, S. K. Korovin, Geometricheskie metody v variatsionnykh zadachakh, Izd-vo Magistr, M., 1998 | MR

[12] J. P. Gossez, “Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficient”, Trans. Amer. Math. Soc., 190 (1974), 163–205 | DOI | MR | Zbl

[13] S. L. Trojanski, “On Locally uniform convex and differentiable norms in certain nonseparable Banach spaces”, Studia Math., 37 (1970), 173–180 | MR

[14] L. P. Vlasov, “Approksimativnye svoistva mnozhestv v lineinykh normirovannykh prostranstvakh”, UMN, 28:6 (174) (1973), 3–66 | MR | Zbl

[15] I. V. Skrypnik, Nelineinye ellipticheskie uravneniya vysshego poryadka, Naukova dumka, K., 1973 | MR | Zbl

[16] V. S. Klimov, N. V. Senchakova, “Ob otnositelnom vraschenii mnogoznachnykh potentsialnykh vektornykh polei”, Matem. sb., 182:10 (1991), 1393–1407 | MR | Zbl

[17] Zh.-L. Lions, Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972 | MR | Zbl

[18] V. S. Klimov, “Operatornye vklyucheniya i kvazivariatsionnye neravenstva”, Matem. zametki, 101:5 (2017), 750–767 | DOI | MR | Zbl

[19] F. Klark, Optimizatsiya i negladkii analiz, Nauka, M., 1988 | MR | Zbl

[20] A. V. Dmitruk, A. A. Milyutin, N. P. Osmolovskii, “Teorema Lyusternika i teoriya ekstremuma”, UMN, 35:6(216) (1980), 11–46 | MR | Zbl

[21] A. Dold, Lektsii po algebraicheskoi topologii, Mir, M., 1976 | MR

[22] Dzh. Milnor, A. Uolles, Differentsialnaya topologiya. Nachalnyi kurs, Mir, M., 1972 | MR

[23] V. S. Klimov, “Deformatsii funktsionalov i bifurkatsii ekstremalei”, Matem. zametki, 81:1 (2007), 70–82 | DOI | MR | Zbl