二阶非齐次泛函微分方程的极限圆型的判定

On The Limit Circle Criterion of A Class of Nonhomogeneous Linear Functional Differential Equations of Second Order

本文研究下列二阶非齐次泛函微分方程（ｒ（ｔ）ｘ＇（ｔ））＇＋ｐ（ｔ）ｘ＇（ｔ）＋ｑ１（ｔ）ｘ（ｔ）＋ｑ２（ｔ）ｘ（ｔ－τ）＝ｆ（ｔ）（Ｅ）的极限圆型，借助辅助泛函和两个重要不等式技巧，获得了保证方程（Ｅ）属于极限圆型的判别准则．

This paper considers the following nonhomogereous linear functional equation (r(t)x'(t))'+p(t)x'(t)+q1(t)x(t)+q2(t)x(t-τ)=f(t)(E)with the aid of auxiliary functionals and inequalities.We obtain some sufficient conditions under which equation(E)belongs to the L.S.L.C.