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.


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


Zbl 0716.34021
Full Text: DOI


[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
[5] F. H. Clarke and J. P. Aubin, ?Monotone invariant solutions to differential inclusions,? J. London Math. Soc.,16, No. 2, 357-366 (1977). · Zbl 0405.34049
[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
[8] G. Bouligand, Introduction à la Géometrie Infinitesimale Directe, Gauthier-Villars, Paris (1932).
[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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