Feng De CHEN, De Xian SUN, Jin
In this paper, nonlinear integro- differential equations with both continuous delay and discrete delays of the form x'(t) = A(t,x(t))x(t) + f-∞t C(t,s)x(s)ds +
+ b(t) are considered, where the n × n matrix function A(t,x) and the n-vectors f(t,x),gi(t,x) (i = 1,2, ...,l) are continuous in (t,x) ∑ R × Rn, C(t,s) ∑ C(R ××R, Rn×n). By combining the theory of exponential dichotomies of linear system and the method of functional analysis, some sufficient conditions that guarantee the existence and uniqueness of periodic solution of the systems are obtained. We not only make an essential improvement and extension of the main results but also obtain some new criteria which guarantee the existence and uniqueness of peroidic solution of the sytems; these criteria can not be obtained by the existing methods (see [1-30]).