Asymptotic behaviours of solutions of nonautonomous functional differential equations with infinite delay (Q1323166)

The technique of Lyapunov functions is applied to the analysis of the asymptotic behaviour of the solutions to functional differential equations with unbounded delay \(x'(t)= f(t,x_ t)\), where \(x(t)\in \mathbb{R}^ n\) and \(x_ t(s)= x(t+ s)\), \(s\leq 0\). The asymptotic behaviour is described in terms of certain functions in the state \(x(t)\) and corresponds to stability in part of the components of \(x(t)\).