Levitan Almost Periodic and Almost Automorphic Solutions of <Emphasis Type="Italic">V</Emphasis>-monotone Differential Equations |
| |
Authors: | David N Cheban |
| |
Institution: | (1) Faculty of Mathematics and Informatics, State University of Moldova, A. Mateevich Street 60, 2009 Chişinău, Moldova |
| |
Abstract: | In the present article we consider a special class of equations
when the function (E is a strictly convex Banach space) is V-monotone with respect to (w.r.t.) , i.e. there exists a continuous non-negative function , which equals to zero only on the diagonal, so that the numerical function α(t):= V(x
1(t), x
2(t)) is non-increasing w.r.t. , where x
1(t) and x
2(t) are two arbitrary solutions of (1) defined on . The main result of this article states that every V-monotone Levitan almost periodic (almost automorphic, Bohr almost periodic) Eq. (1) with bounded solutions admits at least
one Levitan almost periodic (almost automorphic, Bohr almost periodic) solution. In particulary, we obtain some new criterions
of existence of almost recurrent (Levitan almost periodic, almost automophic, recurrent in the sense of Birkgoff) solutions
of forced vectorial Liénard equations.
|
| |
Keywords: | V-monotone system non-autonomous dynamical system skew-product flow Levitan almost periodic and almost automorphic solutions |
本文献已被 SpringerLink 等数据库收录! |
|