一类周期差分微分方程的解

Solutions of a class of periodic difference differential equations

运用一些分析技巧 ,讨论纯量周期差分微分方程x(t) =a(t) x(t) +b(t) x(t- kω)的解 ,其中 a(t) ,b(t)是以ω为周期的连续周期函数 ,k为某自然数 .得到了该方程具有趋于零快于任何指数但最终不恒等于零的解的充分必要条件 .

By using some analytic skills,the solutions of a scalar RDDE(t)=a(t)x(t)+b(t)x(t-kω)is discussed,where a(t),b(t) are the periodic functions of period ω , k is a natural number The necessary and sufficient condition for the equation has the solutions approaching zero faster than any exponential but not identical to zero at last is obtained.The expressions of the solutions are given in details.$$$$