Inverse Scattering Problem for a Piecewise Continuous Sturm - Liouville Equation with Eigenparameter Dependence in the Boundary Conditon

具有依赖于特征参数的边界条件的 Sturm-Liouville 逆问题的一致稳定性

Uniform stability for the inverse Sturm-Liouville problem with eigenparameter-dependent boundary conditions

针对边界条件依赖特征参数的自伴 Sturm-Liouville 算子束，本文利用 Darboux 型变换及其 Lipschitz 连续性，首次证明正、逆谱问题的一致稳定性，并给出有限数据逼近的稳定性估计。

Sturm-Liouville problems with transfer condition Herglotz dependent on the eigenparameter -- Hilbert space formulation

We consider a Sturm-Liouville equation $\ell y:=-y'' + qy = λy$ on the intervals $(-a,0)$ and $(0,b)$ with $a,b>0$ and $q \in L^2(-a,b)$. We impose boundary conditions $y(-a)\cosα= y'(-a)\sinα$, $y(b)\cosβ= y'(b)\sinβ$, where $α\in [0,π)$ and $β\in (0,π]$, together with transmission conditions rationally-dependent on the eigenparameter via \begin{align*} -y(0^+)\left(λη-ξ-\sum\limits_{i=1}^{N} \frac{b_i^2}{λ-c_i}\right) &= y'(0^+) - y'(0^-),\\ y'(0^-)\left(λκ+ζ-\sum\limits_{j=1}^{M}\frac{a_j^2}{λ-d_j}\right) &= y(0^+) - y(0^-), \end{align*} with $b_i, a_j>0$ for $i=1,\dots,N,$ and $j=1,\dots,M…

边界条件线性依赖于谱参数的Sturm-Liouville问题根函数的最小性

Minimality of the root functions of Sturm-Liouville problems with a boundary condition depending linearly on an eigenparameter

研究边界条件线性含谱参数的Sturm-Liouville问题，通过特征函数获得双正交系和特殊伴随函数的显式表示，将根函数系的基与最小性准则重述为特征函数及其导数在特征值处的条件，简化了具体问题的分析。

Resolvent Operator and Eigenfunctions of a Sturm-Liouville Type problem

In this work we investigate the resolvent operator and completeness of eigenfunctions of a Sturm-Liouville problem with discontinuities at two points. The problem contains an eigenparameter in the one of boundary conditions. For operator-theoretic formulation of the considered problem we define an equivalent inner product in the Hilbert space and suitable self-adjoint lineer operator in it.

Uniqueness for Inverse Sturm-Liouville Problems with a Finite Number of Transmission Conditions

We establish various uniqueness results for inverse spectral problems of Sturm-Liouville operators with a finite number of discontinuities at interior points at which we impose the usual transmission conditions. We consider both the case of classical Robin and of eigenparameter dependent boundary conditions.