An asymptotic method of constructing periodic solutions is developed for differential equations of the $n$-th order containing a small parameter. The method makes use of expansions in integral powers of the small parameter. A method of investigating the stability of the resulting solutions is presented. The convergence of the expansions is proved.
Citation Example:Bogolyubov N. N., Sadovnikov B. I. On periodic solutions of differential equations of the $n$-th order with a small parameter // Ukr. Mat. Zh. - 1961. - 13, № 3. - pp. 3-12.