On the multiplicity of eigenvalues of a vectorial Sturm-Liouville differential equation and some related spectral problems

被引：11

作者：

Shen, CL ^{[1
]}

Shieh, CT ^{[1
]}

机构：

[1] Natl Tsing Hua Univ, Dept Math, Hsinchu 30043, Taiwan

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1999年 / 127卷 / 10期

关键词：

vectorial Sturm-Liouville differential equations; eigenvalues; multiplicity; spectrum; potential equations; string equations; Bessel functions;

D O I：

10.1090/S0002-9939-99-05031-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that under certain conditions, a vectorial Sturm-Liouville differential equation of dimension n greater than or equal to 2 can only possess finitely many eigenvalues which have multiplicity n. For the case n = 2, we find a sufficient condition on the potential function Q(x), and a bound m(Q) depending on Q(x), such that the eigenvalues of the equation with index exceeding mQ are all simple. These results are applied to find some sufficient conditions which imply that the spectra of two potential equations, or two string equations, have finitely many elements in common, and an estimate of the number of elements in the intersection of two spectra is provided.

引用

页码：2943 / 2952

页数：10