线性Voltera方程的周期解

Periodic Solutions of Linear Volterra Equations

运用傅氏分析的方法，分别得到了具有以下形式的纯量微分积分方程ｘ′（ｔ）＝∫∞０ｘ（ｔ－ｓ）ｄＥ（ｓ）＋ｆ（ｔ）有唯一的Ｔ周期解、有无穷多个Ｔ周期解和无任何Ｔ周期解的充分必要条件，并得到了该方程的Ｔ周期解的级数形式的表达式．

By using Fourier method, the sufficient and necessary conditions for unique existence of T -periodic solution and existence of infinite many T -periodic solutions of the followng scalar integral-differential equations x′(t)=∫ ∞ 0 x(t-s) d E(s)+f(t) are given.The series expressions of the T -periodic solutions are also given.