Bounded solutions of differential inclusions with homogeneous principal parts
Izvestiya. Mathematics , Tome 64 (2000) no. 4, pp. 755-776.

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We formulate conditions for the existence of stationary and bounded solutions of differential inclusions with homogeneous principal parts and establish formulae for the calculation of the index of the zero singular point of a homogeneous multivalued vector field.
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V. S. Klimov. Bounded solutions of differential inclusions with homogeneous principal parts. Izvestiya. Mathematics , Tome 64 (2000) no. 4, pp. 755-776. http://geodesic.mathdoc.fr/item/IM2_2000_64_4_a2/

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

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

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

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

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

[6] Skrypnik I. V., Nelineinye ellipticheskie uravneniya vysshego poryadka, Nauk. dumka, Kiev, 1973 | MR

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

[8] Mukhamadiev E., “Ogranichennye resheniya i gomotopicheskie invarianty sistem nelineinykh differentsialnykh uravnenii”, Dokl. RAN, 351:5 (1996), 596–598 | MR | Zbl

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

[10] Massi U., Teoriya gomologii i kogomologii, Mir, M., 1981 | MR

[11] Stinrod N., Eilenberg S., Osnovaniya algebraicheskoi topologii, IL, M., 1958

[12] Gaevskii G., Grëger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978 | MR

[13] Klimov V. S., “K zadache o periodicheskikh resheniyakh operatornykh differentsialnykh vklyuchenii”, Izv. AN SSSR. Ser. matem., 53:2 (1989), 309–327 | MR

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

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

[16] Skrypnik I. V., “Razreshimost i svoistva reshenii nelineinykh ellipticheskikh uravnenii”, Sovremennye problemy matematiki, 9 (1976), 131–254 | Zbl

[17] Klimov V. S., “Evolyutsionnye parabolicheskie neravenstva s mnogoznachnymi operatorami”, Matem. sb., 184:8 (1993), 37–54 | MR | Zbl

[18] Klimov V. S., “Ob operatore sdviga po traektoriyam parabolicheskikh vklyuchenii”, Diff. uravn., 31:10 (1995), 1719–1724 | MR

[19] Dubinskii Yu. A., “Nelineinye ellipticheskie i parabolicheskie uravneniya”, Itogi nauki i tekhniki. Sovremennye problemy matematiki, 9, 1976, 5–130 | Zbl

[20] Krasovskii N. N., Nekotorye zadachi teorii ustoichivosti dvizheniya, Fizmatgiz, M., 1959 | MR

[21] Castaing C., Valadier M., Convex analysis and measurable multifunctions, Lecture Notes in Math., no. 580, Springer, Berlin, 1977 | MR | Zbl

[22] Nechas I., “O diskretnosti spektra nelineinogo uravneniya Shturma–Liuvillya”, DAN SSSR, 201:5 (1971), 1045–1048 | MR | Zbl

[23] Levitan B. M., Zhikov V. V., Pochti periodicheskie funktsii i differentsialnye uravneniya, Izd-vo MGU, M., 1978 | MR | Zbl

[24] Pankov A. A., Ogranichennye i pochti periodicheskie resheniya nelineinykh differentsialno-operatornykh uravnenii, Nauk. dumka, Kiev, 1985 | MR

[25] Fučik S., Nečas J., Souček J., Souček V., Spectral analysis of nonlinear operators, Lecture Notes in Mathematics, no. 346, Springer, Berlin, 1973 | MR