Inverse nodal problems for Dirac-type integro-differential operators

Reconstruction of the Dirac-Type Integro-Differential Operator from Nodal Data

The inverse nodal problem for Dirac type integro-differential operator with the spectral parameter in the boundary conditions is studied. We prove that dense subset of the nodal points determines the coefficients of differential part of operator and gives partial information for integral part of it.

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.

An inverse problem for the integro-differential Dirac system with partial information given on the convolution kernel

An integro-differential Dirac system with an integral term in the form of convolution is considered. We suppose that the convolution kernel is known a priori on a part of the interval, and recover it on the remaining part, using a part of the spectrum. We prove the uniqueness theorem, provide an algorithm for the solution of the inverse problem together with necessary and sufficient conditions for its solvability.

On the Lipschitz stability of inverse nodal problem for dirac equation

Inverse nodal problem on Dirac operator is finding the parameters in the boundary conditions, the number m and the potential function V in the Dirac equations by using a set of nodal points of a component of two component vector eigenfunctions as the given spectral data. In this study, we solve a stability problem using nodal set of vector eigenfunctions and show that space of all V functions is homeomorphic to the partition set of all space of asymptotically equivalent nodal sequences induced by an equivalence relation. Furthermore, we give a reconstruction formula for the potential function …

带跳跃条件的 Dirac 微分算子的逆结点问题

Inverse nodal problems for Dirac differential operators with jump condition

本文研究了带跳跃条件的 Dirac 微分算子的逆结点问题，提出求解渐近表达式的新方法，证明系数可由结点稠密子集唯一确定，并给出构造解的算法。

The inverse approach to Dirac-type systems based on the $A$-function concept

The principal objective in this paper is a new inverse approach to general Dirac-type systems modeled after B. Simon's 1999 inverse approach to half-line Schrödinger operators. In particular, we derive the so-called A-equation associated to Dirac-type systems and, given a fundamental positivity condition, we prove that this integro-differential equation for A is uniquely solvable. We show how to recover the matrix-valued potential coefficient from A. This approach is also applicable to matrix-valued Schrödinger operators on a half-line.