ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

1991 MS Classification: 34 Tkachenko, Victor I., Institute of mathematics, Kiev, Ukraine On linear almost periodic systems with bounded solutions We consider a system of linear differential equations dx/dt = A(t)x (1), where x ∈ C^{n}, matrix A(t) is Bohr almost periodic (a. p.). We prove the existence of a system (1) which has nontrivial bounded (but not a. p.) solutions and is such that all the systems from some neighbourhood of it (in uniform on real axis topology of functions A(t)) have not nontrivial a. p. solutions. If the matrix A(t) is skew-adjoint then in every neighbourhood of the system (1) there exists a system possessing all a. p. solutions. Reference: 1. V. I. Tkachenko, On linear almost periodic systems with bounded solutions, Bull. Austral. Math. Soc. 55 (1997), 177–184.

2. V. I. Tkachenko, On linear homogeneous almost periodic systems satisfying the Favard condition, Ukrain. Math. J. 50 (1998), 409–413.