一类三阶变时滞泛函微分方程周期解的存在唯一性

Existence and Uniqueness of Periodic Solution Problems for a Third Order Functional Differental Equation with Delays

利用重合度理论,研究一类具有偏差变元的三阶变时滞微分方程xm(t)+∑2 i=1[aix(i)(t)+bix(i)(t-τi(t))]+cx(t)+g1(x(t))+g2(x(t-τ3(t)))=e(t)的T-周期解问题,得到了上述方程T-周期解存在唯一性的若干结果,所得结果与方程的3个时滞有关.

A type of third order functional differential equation with change delaysx^m（t）＋∑^2 i=1[aix^（i）（t-Ti（t））]＋cx（t）＋g1（x（t））＋g2（x（t-T3（t）））=e（t）was considered by means of the theory of coincide degree. The sufficient condition for the existence of unique T-periodic solution was obtained. The conclusion is relevant to three delays.