On Yu.A. Mitropol'skii's theorem on periodic solutions of systems of nonlinear differential equations with nondifferentiable right-hand sides

A. Buicǎ, J. Llibre, O. Yu Makarenkov

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)

Abstract

A study was conducted to investigate the existence, uniqueness, and asymptotic stability of Mitropol'skii's theorem on periodic solutions of systems of nonlinear differential equations, with nondifferentiable right-hand sides. It is essential to study MAtropol'skii's theorem, as it is noticed that some applications require the generalization of Bogolyubov's second theorem for perturbations, satisfying the Lipschitz conditions. The study also revealed that Mitropol'skii's theorem was generalized and analogues of his uniqueness result from equations with monotone nonlinearities.
Original languageEnglish
Pages (from-to)525-527
JournalDoklady Mathematics
Volume78
Issue number1
DOIs
Publication statusPublished - 1 Aug 2008

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