Inverse nodal problem for the integro-differential Dirac operator with a delay in the kernel

Abstract

‎In the present article‎, ‎we consider an integro-differential Dirac system with an integral delay on a finite interval‎. ‎We obtain the asymptotical formula for the nodal points of the first components of the eigenfunctions‎, ‎formulate a uniqueness theorem and prove that the kernel of the Dirac operator can be uniquely determined from a dense subset of the nodal set‎. We also present examples for reconstructing the kernel by using the nodal points‎.