caa a22 4500 475741587 CHVBK 20180406123500.0 cr unu---uuuuu 170329e20000601xx s 000 0 eng 10.1007/BF02675624 doi (NATIONALLICENCE)springer-10.1007/BF02675624 Gerko A. Moldovan State University, USSR aut Asymptotically recurrent solutions of β -differential equations [Elektronische Daten] [A. Gerko] In the paper methods from the theory of extensions of dynamical systems are used to studyβ-differential equations whose solutions possess the uniqueness property and depend continuously on the initial data and on the right-hand side of the equation. The Zhikov-Bronshtein theorems concerning asymptotically almost periodic solutions of ordinary differential equations are extended toβ-differential equations (in particular, to total differential equations). Along with asymptotic almost periodicity, we also consider asymptotic recurrence, weak asymptotic distality, and asymptotic distality. To the equations we associate dynamical systems generated by the space of the right-hand sides and the spaces of the solutions and of the initial data of solutions of the equation. Generally, the phase semigroups of the dynamical systems are not locally compact. Kluwer Academic/Plenum Publishers, 2000 β -differential equations nationallicence dynamical system nationallicence transformation semigroup nationallicence almost periodic functions nationallicence recurrent functions nationallicence distal functions nationallicence Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/6(2000-06-01), 707-717 0001-4346 67:6<707 2000 67 11006 https://doi.org/10.1007/BF02675624 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02675624 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Gerko A. Moldovan State University, USSR aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/6(2000-06-01), 707-717 0001-4346 67:6<707 2000 67 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer