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On the existence of solutions of a class of differential inclusions on a compact set. (English. Russian original) Zbl 0727.34017

Sib. Math. J. 31, No. 5, 727-732 (1990); translation from Sib. Mat. Zh. 31, No. 5(183), 24-30 (1990).
See the review in Zbl 0716.34021.

MSC:

34A60 Ordinary differential inclusions
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34G99 Differential equations in abstract spaces
47H10 Fixed-point theorems

Citations:

Zbl 0716.34021
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References:

[1] J. P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, Berlin-New York (1984). · Zbl 0538.34007
[2] J. A. Yorke, ?Invariance for contingent equations,? in: Lectures Notes in Operations Research and Math. Economics, Vol. 12, Springer-Verlag, Berlin (1969), pp. 379-381.
[3] B. Cornet, ?Existence of slow solutions for a class of differential inclusions,? J. Math. Anal. Appl.,96, No. 1, 130-147 (1983). · Zbl 0558.34011
[4] G. Haddad, ?Monotone trajectories of differential inclusions and functional differential inclusions with memory,? Israel J. Math.,39, Nos. 1-2, 83-100 (1981). · Zbl 0462.34048
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[6] C. Bardaro and P. Pucci, ?Some contributions to the theory of multivalued differential equations,? Atti Sem. Mat. Fiz. Univ. Modena,32, No. 1, 175-202 (1983). · Zbl 0542.34009
[7] A. Bressan, ?Solutions of lower semicontinuous differential inclusions on closed sets,? Rend. Sem. Math. Univ. Padova,69, 99-107 (1983). · Zbl 0524.34015
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[9] J. P. Aubin and I. Ekeland, Applied Nonlinear Analysis, J. Wiley-Interscience, New York (1984). · Zbl 0641.47066
[10] L. Schwartz, Analyse. I, Hermann, Paris (1967).
[11] A. Fryszkowski, ?Continuous selections for a class of nonconvex multivalued maps,? Studia Math.,76, No. 2, 163-174 (1983). · Zbl 0534.28003
[12] A. Bressan and G. Colombo, ?Extensions and selections of maps with decomposable values,? Studia Math.,90, No. 1, 69-86 (1988). · Zbl 0677.54013
[13] C. J. Himmelberg, ?Measurable relations,? Fund. Math.,87, No. 1, 53-72 (1975). · Zbl 0296.28003
[14] R. H. Martin, Nonlinear Operators and Differential Equations in Banach Spaces, J. Wiley-Interscience, New York (1976). · Zbl 0333.47023
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