Set-valued random differential equations in Banach space
Mariusz Michta
Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 15 (1995), p. 191-200 / Harvested from The Polish Digital Mathematics Library
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We consider the problem of the existence of solutions of the random set-valued equation: (I) DHXt=F(t,Xt)P.1, t ∈ [0,T] -a.e.; X₀ = U p.1 where F and U are given random set-valued mappings with values in the space Kc(E), of all nonempty, compact and convex subsets of the separable Banach space E. Under certain restrictions on F we obtain existence of solutions of the problem (I). The connections between solutions of (I) and solutions of random differential inclusions are investigated.

Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:275974 
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     year = {1995},
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     zbl = {0878.34013},
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Mariusz Michta. Set-valued random differential equations in Banach space. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 15 (1995) pp. 191-200. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-div15i2n6bwm/

[000] [1] J. Banaś, K. Goebel, Measures of noncompactness in Banach spaces, M. Dakkera 1980. | Zbl 0441.47056

[001] [2] F.S. De Blasi, F. Iervolino, Euler method for differential equation with compact, convex valued solutions, Boll. U. M. I. 4 (4) (1971), 941-949. | Zbl 0282.34007

[002] [3] F.S. De Blasi, F. Iervolino, Equazioni differenziali con soluzini a valore compatto convesso, Boll. U. M. I. 2 (4) (1969), 501-591. | Zbl 0195.38501

[003] [4] F. Hiai, H. Umegaki, Integrals, conditional expectation and martingales of multivalued functions, J. Multiv. Anal. 7 (1977), 149-182. | Zbl 0368.60006

[004] [5] C.J. Himmelberg, F.S. Van Vleck, The Hausdorff metric and measurable selections, Topology and its Appl. North-Holland 20 (1985), 121-133. | Zbl 0586.28009

[005] [6] D.A. Kandilakis, N.S. Papageorgiou, On the existence of solutions of random differential inclusions in Banach space, J. Math. Anal. Appl. 126 (1987),11-23. | Zbl 0629.60075

[006] [7] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluver 1991. | Zbl 0731.49001

[007] [8] M. Kisielewicz, Method of averaging for differential equation with compact convex valued solutions, Rend. di. Matem. serie VI, 9 (3) (1976), 1-12.

[008] [9] M. Kisielewicz, B. Serafin, W. Sosulski, Existence theorem for functional-differential equation with compact convex valued solutions, Demmonstratio Math. IX (2) (1976), 229-237. | Zbl 0332.34062

[009] [10] K. Kuratowski, Cz. Ryll-Nardzewski, A general theorem on selectors, Bull. Acad. Polon. Sci, Ser. Sci Math. Astronom. Phys. 13 (1965), 397-403. | Zbl 0152.21403

[010] [11] P. Lopes Pinto, F.S. De Blasi, F. Iervolino, Uniqueness and existence theorem for differential equations with compact convex valued solutions, Boll. U. M. I. 4 (1970), 45-54. | Zbl 0211.12103

[011] [12] M. Michta, Istnienie i jednoznaczność rozwiązań losowych równań różniczkowych o wielowartościowych, zwartych i wypukłych prawych stronach, Praca dokt. UAM Poznań, WSI Zielona Góra (1993).

[012] [13] A. Nowak, Random differential inclusions:measurable selection approach, Ann. Polon. Math. XLIX (1989), 291-296. | Zbl 0674.60062

[013] [14] A. Tołstonogow, Differencjalnyje wkluczenija w Banachowych prostranstwach, Nauka 1986.