Dependence of eigenvalues of a class of fourth-order Sturm-Liouville problems on the boundary

作者：Ge, Suqin^*; Wang, Wanyi; Suo, Jianqing

来源：Applied Mathematics and Computation, 2013, 220: 268-276.

DOI：10.1016/j.amc.2013.06.029

• Fourth-order Sturm-Liouville problems
• Boundary condition
• Eigenvalues

In this paper, we consider the dependence of eigenvalues of a class of fourth-order Sturm-Liouville problems on the boundary. We show that the eigenvalues depend not only continuously but smoothly on boundary points, and that the derivative of the nth 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 higher fourth-order Dirichlet eigenvalues march off to plus infinity, this is also true for the first (i.e., lowest) eigenvalue.

• 出版日期2013-9-1
• 单位内蒙古大学