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

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  • Qiuxia Yang
  • Wanyi Wang
  • Xingchao Gao

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.

Suggested Citation

  • Qiuxia Yang & Wanyi Wang & Xingchao Gao, 2015. "Dependence of Eigenvalues of a Class of Higher-Order Sturm-Liouville Problems on the Boundary," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-10, March.
    • Handle: RePEc:hin:jnlmpe:686102
    DOI: 10.1155/2015/686102
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