Geodesic
About One Class of Operators Inclusions
Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 3, pp. 63-72.

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The operator inclusion $0\in A(x) + N(x)$ is studied. The main results refer to the case, when $A$ – a bounded operator of monotone type from a reflexive space into conjugate to it, $N$ – a conevalued operator. No solution criterion of the viewed inclusion is set up. Integer characteristics of multivalued mappings with homotopy invariance and additivity are introduced. Application to the theory of variational inequalities with multivalued operators is identified.
Keywords: operator inclusion, variational inequality, multivalued mapping, vector field, convex set. 
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N. A. Demyankov; V. S. Klimov. About One Class of Operators Inclusions. Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 3, pp. 63-72. http://geodesic.mathdoc.fr/item/MAIS_2012_19_3_a2/

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

[2] Yu. G. Borisovich, B. D. Gelman, A. D. Myshkis, V. V. Obukhovskii, Vvedenie v teoriyu mnogoznachnykh otobrazhenii, Izd-vo Voronezhskogo universiteta, Voronezh, 1986 | MR | Zbl

[3] V. V. Fedorchuk, V. V. Filippov, Obschaya topologiya, Izd-vo Moskovskogo universiteta, M., 1988 | Zbl

[4] E. Michael, “Continous selections”, Ann. Math., 63:2 (1956), 361–381 | DOI | MR

[5] Zh. P. Oben, I. Ekland, Prikladnoi nelineinyi analiz, Mir, M., 1988 | MR

[6] M. A. Krasnoselskii, P. P. Zabreiko, Geometricheskie metody nelineinogo analiza, Nauka, M., 1975 | MR

[7] J. P. Gossez, “Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficient”, Trans. Amer. Math. Soc., 190 (1974), 163–206 | DOI | MR

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

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

[10] S. I. Pokhozhaev, “O razreshimosti nelineinykh uravnenii s nechetnymi operatorami”, Funktsion. analiz i ego pril., 1:3 (1967), 66–73 | MR | Zbl

[11] F. E. Browder, “Pseudo-monotone operators and the direct method of the calculus of variations”, Bull. Arch. Ration. Mech. Anal., 38:4 (1970), 268–277 | DOI | MR | Zbl

[12] N. A. Bobylev, S. V. Emelyanov, S. K. Korovin, Geometricheskie metody v variatsionnykh zadachakh, Magistr, M., 1998

[13] I. P. Ryazantseva, Izbrannye glavy teorii operatorov monotonnogo tipa, Nizhnii Novgorod, 2008

[14] V. S. Klimov, “K zadache o periodicheskikh resheniyakh operatornykh differentsialnykh vklyuchenii”, Izv. AN SSSR. Ser. matematika, 53:2 (1989), 1393–1407

[15] V. S. Klimov, “Topologicheskie kharakteristiki mnogoznachnykh otobrazhenii i lipshitsevykh funktsionalov”, Izv. RAN. Ser. matematika, 72:4 (2008), 97–120 | DOI | MR