Inverse Nodal Problem for Diffusion Operator Which Has Discontinuity

Abstract

This research explores the inverse nodal problem associated with second-order differential operators on a bounded interval, incorporating conditions at a point of discontinuity inside the interval. The study demonstrates that for each discontinuity point d, belonging to R={rπ,r∈(0,1)∩Q} a solution to the inverse nodal problem exists and offers a constructive technique to determine it. In a departure from earlier findings, this article proves the uniqueness of the solution for the scenario where the internal discontinuity point in (0,π) is any of the countably infinite irrational points defined by d_r=rπ,(r∈(0,1)∩Q) . A method for recovering the problem's coefficients using the asymptotics of the nodal points is also included.

Keywords

• Discontinuous conditions
• Nodal points
• Inverse nodal problem

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