摘要

This paper deals with the periodic boundary value problem for nonlinear impulsive functional differential equation @@@ {x'(t) = f(t, x(t), x(alpha(1)(t)), ..., x(alpha(n)(t))) for a.e. t is an element of [0, T], Delta x(t(k)) = I-k(x(t(k))), k = 1, ..., m, x(0) = x(T). @@@ We first present a survey and then obtain new sufficient conditions for the existence of at least one solution by using Mawhin's continuation theorem. Examples are presented to illustrate the main results.