Geodesic
Bogolyubov's theorem under constraints generated by a~lower semicontinuous differential inclusion
Sbornik. Mathematics, Tome 196 (2005) no. 2, pp. 263-285

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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. 
@article{SM_2005_196_2_a5,
     author = {A. A. Tolstonogov},
     title = {Bogolyubov's theorem under constraints generated by a~lower semicontinuous differential inclusion},
     journal = {Sbornik. Mathematics},
     pages = {263--285},
     publisher = {mathdoc},
     volume = {196},
     number = {2},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2005_196_2_a5/}
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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/