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Bogolyubov’s theorem under constraints generated by a lower semicontinuous differential inclusion. (English. Russian original) Zbl 1089.34013

Sb. Math. 196, No. 2, 263-285 (2005); translations from Mat. Sb. 196, No. 2, 117-138 (2005).
The author proves an analogue of the Bogolyubov theorem in the case when the constraint is the solution set of a differential inclusion governed by a compact and nonconvex-valued lower semicontinuous multifunction. Using this result, he studies the relationship between the solutions of a minimizing problem for a nonconvex integrand on the solution set of a differential inclusion and the minimization of the same integrand on the solution set of the corresponding relaxation problem.

MSC:

34A60 Ordinary differential inclusions
49J24 Optimal control problems with differential inclusions (existence) (MSC2000)
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