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arXiv · 1903.07794

On the Second-order Frechet Derivatives of Eigenvalues of Sturm-Liouville Problems in Potentials

Shuyuan Guo·Guixin Xu·Meirong Zhang
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Abstract

The works of V. A. Vinokurov have shown that eigenvalues and normalized eigenfunctions of Sturm-Liouville problems are analytic in potentials, considered as mappings from the Lebesgue space to the space of real numbers and the Banach space of continuous functions respectively. Moreover, the first-order Frechet derivatives are known and paly an important role in many problems. In this paper, we will find the second-order Frechet derivatives of eigenvalues in potentials, which are also proved to be negative definite quadratic forms for some cases.

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Shuyuan Guo, Guixin Xu, Meirong Zhang. 2019-03-19. On the Second-order Frechet Derivatives of Eigenvalues of Sturm-Liouville Problems in Potentials. https://arxiv.org/abs/1903.07794

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