Tolstonogov, A. A. 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. Reviewer: Ioan I. Vrabie (Iaşi) Cited in 5 Documents MSC: 34A60 Ordinary differential inclusions 49J24 Optimal control problems with differential inclusions (existence) (MSC2000) Keywords:Bogolyubov theorem; nonconvex constraints; differential inclusion; lower semicontinuous right-hand side; minimization problem PDFBibTeX XMLCite \textit{A. A. Tolstonogov}, Sb. Math. 196, No. 2, 263--285 (2005; Zbl 1089.34013) Full Text: DOI