Geodesic
Bogolyubov's theorem under constraints generated by a lower semicontinuous differential inclusion
Sbornik. Mathematics, Tome 196 (2005) no. 2, pp. 263-285 Cet article a éte moissonné depuis la source Math-Net.Ru

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An analogue of the classical theorem of Bogolyubov with non-convex constraint is proved. The constraint is the solution set of a differential inclusion with non-convex lower semicontinuous right-hand side. As an application we study the interrelation between the solutions of the problem of minimizing an integral functional with non-convex integrand on the solutions of the original inclusion and the solutions of the relaxation problem. 
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A. A. Tolstonogov. Bogolyubov's theorem under constraints generated by a lower semicontinuous differential inclusion. Sbornik. Mathematics, Tome 196 (2005) no. 2, pp. 263-285. http://geodesic.mathdoc.fr/item/SM_2005_196_2_a5/

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