Dependence of Eigenvalues of a Class of Higher-Order Sturm-Liouville Problems on the Boundary

Qiuxia Yang, Wanyi Wang and Xingchao Gao

Mathematical Problems in Engineering, 2015, vol. 2015, 1-10

Abstract:

We show that the eigenvalues of a class of higher-order Sturm-Liouville problems depend not only continuously but also smoothly on boundary points and that the derivative of the th eigenvalue as a function of an endpoint satisfies a first order differential equation. In addition, we prove that as the length of the interval shrinks to zero all th-order Dirichlet eigenvalues march off to plus infinity; this is also true for the first (i.e., lowest) eigenvalue.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:686102

DOI: 10.1155/2015/686102

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