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Extremal selections of multivalued mappings and the ”bang-bang” principle for evolution inclusions. (English. Russian original) Zbl 0784.54024
Sov. Math., Dokl. 43, No. 2, 481-485 (1991); translation from Dokl. Akad. Nauk SSSR 317, No. 3, 589-593 (1991).
The author presents a theorem on the existence of continuous selections of multivalued mappings having the Scorza-Dragoni property. Applications to the question of existence as well as some properties of extremal solutions of certain classes of evolution inclusions in Banach spaces are also given. The facts are announced without proofs.

54C65 Selections in general topology
34A60 Ordinary differential inclusions
54C60 Set-valued maps in general topology
49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)