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Differential inclusions in Banach space with nonconvex right-hand side. The existence of solutions. (English. Russian original) Zbl 0529.34058

Sib. Math. J. 22, 625-637 (1982); translation from Sib. Mat. Zh. 22, 182-198 (1981).

MSC:

34G10 Linear differential equations in abstract spaces
34A40 Differential inequalities involving functions of a single real variable
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34A60 Ordinary differential inclusions
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[1] A. F. Filippov, ?Classical solutions of differential equations with multivalued right-hand side,? Vestn. Mosk. Gos. Univ., Ser. Mat., No. 3, 16-26 (1967).
[2] A. F. Filippov, ?The existence of solutions of multivalued differential equations,? Mat. Zametki,10, No. 3, 307-313 (1971).
[3] A. F. Filippov, ?Conditions for the existence of solutions of multivalued differential equations,? Differents. Uravn.,13, No. 6, 1070-1078 (1977). · Zbl 0364.49014
[4] H. Hermes, ?Continuous and measurable selections and the existence of solutions of generalized differential equations,? Proc. Am. Math. Soc.,29, No. 3, 535-542 (1971). · Zbl 0214.09802
[5] N. Kikuchi and Y. Tomita, ?On the absolute continuity of multifunctions and orientor fields,? Funkcialaj Ekvacoj,14, No. 3, 161-170 (1971). · Zbl 0248.49023
[6] H. Kaczyncki and C. Olech, ?Existence of solutions of orientor fields with nonconvex right-hand side,? Ann. Polon. Math.,29, No. 1, 61-66 (1974). · Zbl 0285.34008
[7] H. A. Antosiewicz and A. Cellina, ?Continuous selections and differential relations,? J. Diff. Equations,19, No. 2, 386-398 (1975). · Zbl 0311.54016
[8] A. M. Mukhsinov, ?Differential inclusions in Banach spaces,? Dokl. Akad. Nauk SSSR,217, No. 4, 759-761 (1974). · Zbl 0313.34069
[9] A. A. Tolstonogov, ?Classical solutions of differential inclusions in Banach spaces with nonconvex right-hand side,? in: Nonlinear Oscillations and Control Theory [in Russian], Vol. 2, Udmurtsk. Univ., Izhevsk (1978), pp. 16-23. · Zbl 0543.34007
[10] A. A. Tolstonogov, ?Differential inclusions in Banach spaces and continuous selectors,? Dokl. Akad. Nauk SSSR,244, No. 5, 1088-1092 (1979).
[11] K. Kuratowski, Topology, Vol. 1, Academic Press (1966).
[12] K. Yosida, Functional Analysis, Springer-Verlag (1974). · Zbl 0286.46002
[13] L. Schwartz, Analysis [Russian translation], Vol. 1, Mir, Moscow (1972).
[14] K. Kuratowskii, Topology, Vol. 2, Academic Press (1969).
[15] R. J. Auman, ?Integrals of set-valued functions,? J. Math. Anal. Appl.,12, No. 1, 1-12 (1965). · Zbl 0163.06301
[16] A. A. Tolstonogoy, ?Support functions of convex compacta,? Mat. Zametki,22, No. 2, 203-212 (1977).
[17] M. Hukuhara, ?Integration des application mesurables dont la valeur est un compact convexe,? Funkcialaj Ekvacoj,10, No. 16, 205-223 (1967). · Zbl 0161.24701
[18] C. J. Himmelberg, ?Measurable relations,? Fund. Math.,87, No. 1, 53-72 (1975). · Zbl 0296.28003
[19] B. N. Sadovskii, ?Limiting compact and condensing operators,? Usp. Mat. Nauk,27, No. 1, 81-146 (1972).
[20] G. S. Goodman, ?On a theorem of Scorza-Dragoni and its applications to optimal control,? in: Mathematical Theory of Control, Academic Press, New York (1967), pp. 222-233.
[21] K. Goebel and W. Rzymowski, ?An existence theorem for the equations x?=f(t,x) in Banach space,? Bull. Acad. Polon. Sci., Ser. Sci., Math., Astr. Phys.,18, No. 7, 367-370 (1970). · Zbl 0202.10003
[22] R. E. Smitson, ?Multifunctions,? Nieuw Arch. Wiskunde,20, No. 3, 31-53 (1972).
[23] C. Olech, ?Existence and uniqueness of solutions of an ordinary differential equation in Banach space,? Bull. Acad. Polon. Sci., Ser. Sci. Math., Astron. Phys.,8, No. 10, 667-673 (1960). · Zbl 0173.35303
[24] R. I. Kozlov, ?The theory of differential equations with discontinuous right-hand sides,? Differents. Uravn.,10, No. 7, 1264-1275 (1974).
[25] C. J. Himmelberg, ?Precompact contraction of metric uniformities and the continuity of F(t,x),? Rend. Sem. Math. Univ. Padova,50, 185-188 (1973). · Zbl 0285.28018
[26] H. A. Antosiewicz and A. Cellina, ?Continuous extensions of multifunctions,? Ann. Polon. Math.,34, No. 1, 108-111 (1977).
[27] S. Szufla, ?Existence of solutions of ordinary differential equations in Banach spaces,? Boll. Unione Mat. Italiana,15A, No. 3, 535-544 (1978). · Zbl 0402.34002
[28] G. Piangiani, ?Existence of solutions of ordinary differential equations in Banach spaces,? Bull. Acad. Polon. Sci., Ser. Sci. Math., Astron. Phys.,23, No. 8, 853-857 (1975).
[29] S. Kato, ?Convergence of successive approximations for nonlinear ordinary differential equations in a Banach space,? Funkcialaj Ekvacoj,21, No. 1, 43-52 (1978). · Zbl 0391.34039
[30] S. Szufla, ?On the equation x?=f(t,x) in Banach spaces,? Bull. Acad. Polon. Sci., Ser. Sci. Math., Astron. Phys.,26, No. 5, 401-406 (1978). · Zbl 0417.34096
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