Abstract
In the present study, the inverse nodal problem is discussed for the discontinuous periodic (or anti-periodic) Sturm–Liouville problem. Such types of problems are different from regular problems because of discontinuity in the boundary conditions. Firstly, results of the Sturm–Liouville problem including jump condition are present. Then, by deferring the zeros of eigenfunctions, the inverse problem is solved as we desired. The method is based on considering a translation so that the periodic (or anti-periodic) problem is reduced to a Dirichlet problem as in Cheng and Law (Inverse Prob 22: 891–901, 2006). But, our problem including also discontinuous conditions. In addition to all of these, although there are so many results on this subject, we combine both periodic conditions and discontinuity.
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