正则型Sturm-Liouville微分算子特征值关于边界条件的连续依赖性

Continuous Dependence of Eigenvalues of Regular Sturm-Liouville Differential Operators on the Boundary Condition

本文以隐函数存在定理为主要工具,重新研究Sturm-Liouville微分算子特征值关于边界条件参数的连续依赖性问题.我们不仅给出了该结果一个简单的新证明,而且明确地呈现了第n个特征值关于边界条件参数的导数,进而得到了在实耦合型边界条件下二重特征值产生的位置及个数的新结果.

In this paper,we study the continuous dependence of eigenvalue of Sturm-Liouville differential operators on the boundary condition by using of implicit function theorem.The work not only provides a new and elementa.ry proof of the above results,but also explicitly presents the expressions for derivatives of the n-th eigenvalue with respect to given parameters.Furthermore,we obtain the new results of the position and number of the generated double eigenvalues under the real coupled boundary condition.