Inverse Nodal Problems for Dirac-Type Integro-Differential Operators with Linear Functions in the Boundary Condition

Abstract

In this article, Dirac-type integro-differential operator with linear functions in the boundary condition is considered. We obtain asymptotic expressions for the solution of the differential system and derive the large eigenvalues and nodal points. We also give a constructive procedure for solving an inverse nodal problem. We prove that a dense subset of the nodes determines the coefficients of the differential part of the operator and gives partial information for the integral part of it.

Keywords:

• Dirac operator
• integral-differential operators
• inverse nodal problem
• uniqueness theorem
• spectral problems

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• 34A55
• 34L05
• 34K29
• 34K10
• 47G20

Acknowledgment

The authors would like to express their gratitude to the editor and anonymous referees for their helpful comments which significantly improved the quality of the article.