On the uniqueness of the solution of dual equation of a singular Sturm-Liouville problem

In this paper we consider differential systems having a singularity and one turning point. First, by a replacement, we transform the system to a linear second-order equation of Sturm-Liouville type with a singularity. Using the infinite product representation of solutions provided in [8], we obtain the dual equation, then we investigate the uniqueness of the solution for the dual equation of the inverse spectral problem of Sturm-Liouville equation. This result is necessary for expressing inverse problem of indefinite Sturm-Liouville equation.