Abstract

A node of a Sturm–Liouville problem is an interior zero of an eigenfunction. The aim of this paper is to present a simple and new proof of the result on sharp bounds of the node for the Sturm–Liouville equation with the Dirichlet boundary condition when the \(L^1\) norm of potentials is given. Based on the outer approximation method, we will reduce this infinite-dimensional optimization problem to the finite-dimensional optimization problem.

中文翻译：

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Sturm-Liouville 方程的节点锐界

摘要

Sturm-Liouville 问题的节点是特征函数的内部零。本文的目的是对具有狄利克雷边界条件的 Sturm-Liouville 方程在给出\ (L^1\)势范数时节点锐界的结果提供一个简单而新的证明。基于外近似法，我们将这个无限维优化问题简化为有限维优化问题。