一类具正系数的四阶对称微分算子的极限点型

On the Limit-point Case of a Class of Fourth-order Ordinary Differential Operators with Positive Coefficients

将形如 L =(py″)″-(qy′)′的微分算式分解为两个二阶微分算式的乘积 ,在 L有正的下界的条件下 ,L的亏指数即是上述两个微分算式的亏指数之和 .从而为这种四阶微分算式的极限点的判别提供了新的简捷的方法 。

Some fourth order ordinary differential expressions are decomposed into the products of two second order ordinary differential expressions,when L has a positive belower bound,the deficiency index of L is the sum of the deficiency indices of the two second order differential expressions.Thus,we proposed a new and concise method for judging the fourth order differential expressions to be limit point case,and gave a new sufficient condition of limit point case.