Almost periodic and almost automorphic solutions of monotone differential equations with a strict monotone first integral

David Cheban

State University of Moldova, Institute of Research and Innovation, Laboratory of "Fundamental and Applied Mathematics" A. Mateevich Street 60, MD-2009 Chişinău, Moldova

Аннотация: The paper is dedicated to the study of problem of Poisson stability (in particular periodicity, quasi-periodicity, Bohr almost periodicity, almost automorphy, Levitan almost periodicity, pseudo-periodicity, almost recurrence in the sense of Bebutov, recurrence in the sense of Birkhoff, pseudo-recurrence, Poisson stability) and asymptotical Poisson stability of motions of monotone non-autonomous differential equations which admit a strict monotone first integral. This problem is solved in the framework of general non-autonomous dynamical systems.

Ключевые слова и фразы: Bohr/Levitan almost periodic and almost automorphic solutions, monotone nonautonomous dynamical systems, first integral.

MSC: 34C12, 34C27, 34D05, 37B20, 37B55, 37B65

Поступила в редакцию: 15.10.2020

Язык публикации: английский