Recovering Dirac Operator with Nonlocal Boundary Conditions

Recovering Nonlocal Differential Pencils

Inverse problems for differential pencils with nonlocal conditions are investigated. Several uniqueness theorems of inverse problems from the Weyl-type function and spectra are proved, which are generalizations of the well-known Weyl function and Borg's inverse problem for the classical Sturm-Liouville operator.

Recovering Differential Operators with Nonlocal Boundary Conditions

Inverse spectral problems for Sturm-Liouville operators with nonlocal boundary conditions are studied. As the main spectral characteristics we introduce the so-called Weyl-type function and two spectra, which are generalizations of the well-known Weyl function and Borg's inverse problem for the classical Sturm-Liouville operator. Two uniqueness theorems of inverse problems from the Weyl-type function and two spectra are presented and proved, respectively.

Recovering Dirac systems with singularities in interior points

We study the non-selfadjoint Dirac system on a finite interval having non-integrable regular singularities in interior points with additional matching conditions at these points. Properties of spectral characteristics are established, and the inverse spectral problem is investigated. We provide a constructive procedure for the solution of the inverse problem, and prove its uniqueness. Moreover, necessary and sufficient conditions for the global solvability of this nonlinear inverse problem are obtained.

关于恢复具有两个延迟的 Dirac 算子

On recovering Dirac operators with two delays

针对含两个常数延迟的 Dirac 型泛函微分算子，本文研究其逆谱问题，并给出由四个谱唯一恢复算子的延迟条件及不可能性边界。

Inverse Nodal Problems for Dirac Type Integro Differential System with a Nonlocal Boundary Condition

In this work, the Dirac-type integro di§erential system with one classical boundary condition and another nonlocal integral boundary condition is considered. We obtain the asymptotic formulae for the solutions, eigenvalues and nodal points. We also investigate the inverse nodal problem and prove that given a dense subset of nodal points uniquely determines the boundary condition parameter and the potential function of the considered di§erential system. We also provide an e§ective procedure for solving the inverse nodal problem.

非局部 $p$-拉普拉斯算子的变分特征值渐进行为研究

Asymptotics of variational eigenvalues for a general nonlocal $p$-Laplacian with varying horizon

本文研究了具有可变视距的通用非局部 $p$-拉普拉斯算子的变分特征值渐进行为，利用 $\Gamma$-收敛论证，分析了视距变化极限情况下的解稳定性，恢复了局部 $p$-拉普拉斯和 $H^{s,p}$-拉普拉斯特征值问题的解。