Inverse nodal problems for Dirac type integro differential system with a nonlocal boundary condition

In this paper, the Dirac-type integro differential system with a nonlocal integral boundary condition is considered. First, we derive the asymptotic expressions for the solutions and large eigenvalues. Second, we provide asymptotic expressions for the nodal points and prove that a dense subset of nodal points uniquely determines the boundary condition parameter and the potential function of the considered differential system. We also provide an effective procedure for solving the inverse nodal problem.