Eigenvalue ratios for the regular Sturm-Liouville system

被引：14

作者：

Huang, YL

Law, CK

机构：

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1996年 / 124卷 / 05期

关键词：

regular Sturm-Liouville system; Neumann boundary conditions; eigenvalue ratio; modified Prufer substitution;

D O I：

10.1090/S0002-9939-96-03396-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Following the method of Ashbaugh-Benguria in Comm. Math. Phys. 124 (1989), 403-415; J. Differential Equations 103 (1993), 205-219, we prove an upper estimate of the arbitrary eigenvalue ratio (mu(m)/mu(n)) for the regular Sturm-Liouville system. This upper estimate is sharp for Neumann boundary conditions. We also discuss the sign of mu(1) and include an elementary proof of a useful trigonometric inequality first given in the aforementioned articles.

引用

页码：1427 / 1436

页数：10

共 4 条

[1] BEST CONSTANT FOR THE RATIO OF THE 1ST 2 EIGENVALUES OF ONE-DIMENSIONAL SCHRODINGER-OPERATORS WITH POSITIVE POTENTIALS [J].