Inverse nodal problem for Sturm-Liouville operator with n-potentials

Spectral theory of differential operators has an important role in science and engineering. One of these operators is Sturm-Lioville operator. There are many results in the literature regarding Sturm-Liouville problem both in terms of direct and inverse problems. However, by adding different conditions to the potential function in the problem, more interesting results that can contribute to the literature can be obtained. In this study, separable boundary conditions are taken into consideration with Sturm-Liouville equation and the solution of the inverse problem is reached with the help of the zeros (nodal points) of the eigenfunctions. Especially, a formula for eigenvalues, nodal points, nodal lengths and potential functions has been found with the help of the Prüfer transformation. We can say that the problem in this study includes different and interesting results from the previous studies in terms of covering more than one potential function.