arXiv subjects

Shuyuan Guo

Publications and source records attributed to Shuyuan Guo.

2 recordsLinked to original sources

arXiv2025

Explicit sharp bounds for all nodes of Sturm-Liouville operators with potentials in $L^1$ balls

For the classical Sturm-Liouville operators, we prove the sharp bounds for all nodes of eigenfunctions by regarding these nodes as nonlinear functionals of potential $q\in L^1[0,1]$. By studying the optimization problems to minimize or to maximize the nodes $\{ T_{i,m}\}$ subject to the constraint $\|q\|_{1}=r$ with $r>0$ and using the strong continuity of the nodes in potentials, we obtain the explicit expressions for the sharp bounds, which are given as elementary functions.

math.SP↗

arXiv2019

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

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.

math.SP↗