Spectral Properties of Sturm-Liouville Problems with Strongly Singular Potentials
Spectral Properties of Sturm-Liouville Problems with Strongly Singular Potentials
复制标题
强奇异势的 Sturm-Liouville 问题的谱性质
DOI：
10.1007/s00025-018-0941-3
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发表时间：
2019
影响因子：
2.2
通讯作者：
Yan Jun
中科院分区：
文献类型：
--
作者：
Liu Yu;Shi Guoliang;Yan Jun
This paper studies a class of singular differential equations $$\begin{aligned} -\left( \frac{\mathrm {d}}{{\mathrm {d}}x}-\frac{k}{x^{l}}-v\right) \left( \frac{{\mathrm {d}}}{{\mathrm {d}}x}+\frac{k}{x^{l}}+v\right) y=\lambda y \text { on }J=(0,1) , \end{aligned}$$whereandwhich is bounded below. Using the prüfer transformation, we get the oscillation property of the eigenfunctions. In particular, the location of eigenvalues are also described. Furthermore, we establish the continuous dependence ofnth eigenvalue on the boundary condition.
This paper studies a class of singular differential equations $$\begin{aligned} -\left( \frac{\mathrm {d}}{{\mathrm {d}}x}-\frac{k}{x^{l}}-v\right) \left( \frac{{\mathrm {d}}}{{\mathrm {d}}x}+\frac{k}{x^{l}}+v\right) y=\lambda y \text { on }J=(0,1) , \end{aligned}$$whereandwhich is bounded below. Using the prüfer transformation, we get the oscillation property of the eigenfunctions. In particular, the location of eigenvalues are also described. Furthermore, we establish the continuous dependence ofnth eigenvalue on the boundary condition.