Periodic solutions of systems of differential equations with random right-hand sides

• Datum: 1997
• Hauptverfasser: Danilov, V. Ya., Martynyuk, D. I., Stanzhitskii, A. N., Данилов, В. Я., Мартынюк, Д. И., Станжицкий, А. Н.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 1997
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/4999
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We prove a theorem on the existence of periodic solutions of a system of differential equations with random right-hand sides and small parameter of the form dx/dt=εX(t, x, ξ(t)) in a neighborhood of the equilibrium state of the averaged deterministic system dx/dt=εX 0(t).