关于修正的第二类Paine-de Hoog-Anderssen边值问题
On modified second Paine-de Hoog-Anderssen boundary value problem
摘要：
本文讨论Sturm-Liouville边值问题的一种特殊情况，即本征值问题，其特征是Sturm-Liouville微分算子具有未知的谱和相应的特征函数.通过研究薛定谔形式的边值问题，我们感兴趣的问题，相应的不变函数采取的形式的倒数二次型。我们称之为修改的第二Paine-de Hoog-Anderssen（PdHA）问题。我们估计的最低阶特征值没有解决的本征值问题，而是利用本地化的景观和有效的势函数代替。虽然对于频谱估计表现出较差质量的参数值的特定组合，但是结果通常是可接受的，尽管它们高估了数值计算。质量，特征值估计是惊人的优秀，该建议可以采用到其他BVP。
英文摘要：
This article deals with a special case of the Sturm-Liouville boundary value problem (BVP), an eigenvalue problem characterized by the Sturm-Liouville differential operator with unknown spectra and the associated eigenfunctions. By examining the BVP in the Schrödinger form, we are interested in the problem where the corresponding invariant function takes the form of a reciprocal quadratic form. We call this BVP the modified second Paine-de Hoog-Anderssen (PdHA) problem. We estimate the lowest-order eigenvalue without solving the eigenvalue problem but by utilizing the localized landscape and effective potential functions instead. While for particular combinations of parameter values that the spectrum estimates exhibit a poor quality, the outcomes are generally acceptable although they overestimate the numerical computations. Qualitatively, the eigenvalue estimate is strikingly excellent, and the proposal can be adopted to other BVPs.
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