一类二阶非齐次时滞微分方程属于L．S∩L．C的判定

The Quadratically Integrability and Boundedness of A Class of Second Order Nonhomogeness Differential Equation With Delay

通过构造泛函，并引入辅助函数Ｆ（ｔ），得到了保证一类二阶非齐次时滞微分方程ｘ″（ｔ）＋ｐ（ｔ）ｘ′（ｔ）＋ｑ１（ｔ）ｘ（ｔ）＋ｑ２（ｔ）ｘ（τ（ｔ））＝ｆ（ｔ）所有解ｘ（ｔ）均满足ｘ（ｔ）∈Ｌ２［ａ，∞）∩Ｌ∞［ａ，∞）的充分条件。

Consider the follow second order nonhomogeneous differential equations with delay, x″(t)+p(t)x′(t)+q 1(t)x(t)+q 2(t)x(τ(t))=f(t)(*) with the aid of auxiliary funcfionals and two fundameental inequalities, some sufficiental concitions under which equation (*) belongs to L 2[a,∞)∩L ∞[a,∞) are obtained.