On the Second-order Frechet Derivatives of Eigenvalues of Sturm-Liouville Problems in Potentials
Spectral Theory
2019-03-20 v1
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.
Keywords
Cite
@article{arxiv.1903.07794,
title = {On the Second-order Frechet Derivatives of Eigenvalues of Sturm-Liouville Problems in Potentials},
author = {Shuyuan Guo and Guixin Xu and Meirong Zhang},
journal= {arXiv preprint arXiv:1903.07794},
year = {2019}
}
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10 pages