# On the Lipschitz stability of inverse nodal problem with discontinuous boundary conditions on finite intervals

Authors Seyfollah Mosazadeh Iranian Journal of Mathematical Sciences and Informatics University of Kashan Full Paper Accepted for publication ISI Typographic Iran, Islamic Republic Of ISI, ISC

## Abstract

‎Inverse nodal problem on Sturm-Liouville operator is finding the potential function $q$ by using the set of nodal points $\{ x^{(n)}_{j} \}$‎. ‎In this paper‎, ‎we consider a Sturm-Liouville boundary value problem with a discontinuity at $\zeta\in (0,1)$ and boundary conditions rationally dependent on the eigenparameter‎, ‎and obtain eigenvalues‎, ‎eigenfunctions and nodal points‎. ‎Then‎, ‎we present the solution of the inverse problem by using the nodal points and prove the Lipschitz stability for the inverse nodal problem