一类中立型积分微分方程周期解的存在性和唯一性

ON THE EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS OF A KIND OF NEUTRAL INTEGRO-DIFFERENTIAL EQUTIONS

考虑具连续时滞和离散时滞的中立型积分微分方程d/(dt)[x(t)+sum from j=1 to q e_j(t)x(t-δ_j(t))]=A(t,x(t))x(t)+integral from -∞to t C(t,s)x(s)ds+sum from i=1 to l gi(t,x(t-τ_i(t)))+b(t)和d/(dt)[x(t)+sum from j=1 to q e_j(t)x(t-δ_j(t))]=A(t)x(t)+integral from -∞to t C(t,s)x(s)ds+sum from i=1 to l gi(t,x(t-τ_i(t)))+b(t)周期解的存在性和唯一性问题,利用线性系统指数型二分性理论和泛函分析方法,并通过技巧性代换获得了保证中立型系统周期解存在性和唯一性的充分性条件,从而避开了在研究中立型系统时x(t-δ)时滞项的导数x′(t-δ)的出现,推广了相关文献的主要结果.

The existence and uniqueness of periodic solutions of neutral integro-differential equations with both continuous and discrete delays of the form dt/d[x（t）＋∑j=1 q ej（t）x（t-δj（t））]=A（t,x（t））x（t）＋∫-∞^t C（t,s）x（s）ds＋∑j=1^1gj（t,x（t-Ti（t）））＋b（t） 和dt/d[x（t）＋∑j=1 q ej（t）x（t-δj（t））]=A（t）x（t）＋∫-∞^t C（t,s）x（s）ds＋∑j=1^1gj（t,x（t-Ti（t）））＋b（t）are considered. 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 system are obtained.