An inverse spectral problem for integro-differential Dirac operators with general convolution kernels

被引：20
作者：
Bondarenko, Natalia [1 ,2 ]
Buterin, Sergey [2 ]
机构：
[1] Samara Natl Res Univ, Dept Appl Math, Samara, Russia
[2] Saratov Natl Res State Univ, Dept Math, Saratov, Russia
来源：
APPLICABLE ANALYSIS | 2020年 / 99卷 / 04期
基金：
俄罗斯科学基金会;
关键词：
Yongzhi Xu; Non-selfadjoint Dirac system; integro-differential operator; nonlocal operator; inverse spectral problem; nonlinear integral equation;
D O I：
10.1080/00036811.2018.1508653
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An integro-differential Dirac system with a convolution kernel consisting of four independent functions is considered. We prove that the kernel is uniquely determined by specifying the spectra of two boundary value problems with one common boundary condition. The proof is based on the reduction of this nonlinear inverse problem to solving some nonlinear integral equation, which we solve globally. On this basis we also obtain a constructive procedure for solving the inverse problem along with necessary and sufficient conditions for its solvability in an appropriate class of kernels.
引用
收藏
页码：700 / 716
页数：17
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