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

@article{Ge2013DependenceOE,
  title={Dependence of eigenvalues of a class of fourth-order Sturm-Liouville problems on the boundary},
  author={Suqin Ge and Wanyi Wang and Jianqing Suo},
  journal={Applied Mathematics and Computation},
  year={2013},
  volume={220},
  pages={268-276}
}
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… CONTINUE READING

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