一类Sturm-Liouville问题特征的渐近分析

Asymptotic Behavior of Eigenvalues of a Sturm-Liouville Problem with Robin Boundary

考虑[0,1]上带第三类边界条件的S-L问题特征值的渐近表示.利用已有的渐近性结果及Fr啨chet导数技术,对特征值进行了精细的分析,清楚地给出了边界条件中的常数(h,H)对特征值的影响.本文的工作对S-L问题的一类反谱问题及相关微分方程反问题的唯一性结果有着重要的应用,也为专著[4,6]中的某些关键结果提供了一个简化的证明途径.

In this paper,we consider the asymptotic expansion of eigenvalues for a kind of Sturm-Liouville problems in [0,1] with Robin boundary conditions. By combining the known asymptotic theory and Frfichet derivative technique together,we give a sophisticated analysis for the eigenvalues,which reveals the explicit effect of boundary impedance on eigenvalues. The application of the results in this paper is to study the uniqueness of a kind of inverse spetral problems and some related inverse problems for partial differential equations.