Inverse nodal problem for polynomial pencil of Sturm-Liouville operator

Abstract

The paper is about boundary value problem for polynomial pencil of Sturm-Liouville operators. Especially, we find all coefficients of the operator by using nodal points (zeros of eigenfunctions). Regularly, we find eigenvalues, nodal points, and nodal lengths by Prufer substitution. These results are used to give a reconstruction formula for all complex functions q(d)(x), d = (0,n-1) over bar which are known potentials in the theory. However, method is similar with some papers; our resultsmore general then because of including many potential functions.