Total stability property in limiting equations for a functional differential equation with infinite delay. (English) Zbl 0599.34071

Hino, Yoshiyuki; Yoshizawa, Taro

Čas. Pěst. Mat. 111, 62-69 (1986).

A. D’Anna [Funk. Ekvacioj, Ser. Int. 27, 201-209 (1984; Zbl 0556.34054)] has shown that the total stability of a bounded solution can be deduced from the total stability in a certain limiting equation which is obtained by employing the Bohr topology. In this article, the authors have extended D’Anna’s results to functional differential equations with infinite delay, where the arguments in ordinary differential equations cannot be applied since the phase spaces are not locally compact.

MSC:

34D20

Stability of solutions to ordinary differential equations

Keywords:

limiting equation; total stability of a bounded solution; Bohr topology; functional differential equations with infinite delay; phase spaces

Citations:

Zbl 0556.34054