论文标题
Sturm-Liouville方程的零dirac加权特征值，具有可集成的电位，并且应用于反问题
The number of Dirac-weighted eigenvalues of Sturm-Liouville equations with integrable potentials and an application to inverse problems
论文作者
论文摘要
在本文中，我们通过计算dirichlet边界条件下配备了一般的集成电位和狄拉克权重的Sturm-Liouville方程的加权特征值的数量来进一步。我们表明，对于具有一般整合电位的Sturm-Liouville方程式，如果其重量是$ n $ dirac dilac delta函数的正线性组合，那么它最多具有$ n $（可能小于$ n $，甚至是$ n $，甚至是$ 0 $ $ 0 $），或者是独特的真实dirichlet eigenlet eigenvalues，或者每个复杂的数字都是dirichlet eigenlet eigenlet eigenvalue;特别是，在某种鲜明的条件下，Dirichlet Eigenvalues的数量正好为$ n $。我们的主要方法是介绍特征矩阵和特征的特性概念，以解决dirac重量的Sturm-Liouville问题，并提出了用于计算特征值的一般和直接算法。作为应用程序，研究了一类用于涉及单个狄拉克分布权重的Sturm-liouville方程的逆Dirichelt问题。
In this paper, we further Meirong Zhang, et al.'s work by computing the number of weighted eigenvalues for Sturm-Liouville equations, equipped with general integrable potentials and Dirac weights, under Dirichlet boundary condition. We show that, for a Sturm-Liouville equation with a general integrable potential, if its weight is a positive linear combination of $n$ Dirac Delta functions, then it has at most $n$ (may be less than $n$, or even be $0$) distinct real Dirichlet eigenvalues, or every complex number is a Dirichlet eigenvalue; in particular, under some sharp condition, the number of Dirichlet eigenvalues is exactly $n$. Our main method is to introduce the concepts of characteristics matrix and characteristics polynomial for Sturm-Liouville problem with Dirac weights, and put forward a general and direct algorithm used for computing eigenvalues. As an application, a class of inverse Dirichelt problems for Sturm-Liouville equations involving single Dirac distribution weights is studied.
