On the stability problem for functional differential equations with infinite delay (Q735864)

The paper is devoted to the problem of stability of functional differential equations with infinite delay. The study is based on the limiting equations approach and Lyapunov's direct method. A theorem on localization of a positive limit set is established and four theorems on stability are stated in terms of Lyapunov functional of constant sign with a derivative of constant sign. The theorems are proved by using some results derived by \textit{N. O. Sedova} in [Differ. Equ. 38, No.~10, 1423--1434 (2002; Zbl 1036.34089)]. An illustrative example is given.