Characteristic Parameter Polynomial Boundary Conditions Of Sturm-liouville Equation Inverse Node Problem

Inverse nodal problem consists in constructing operators from the given nodes of their eigen-functions. In this paper, the Sturm-Liouville problem with boundary conditions depending polynomially on the spectral parameter is studied. From 1950s, mathematicians found that the spectral parameter appears not only in the equation, but also in the boundary conditions in most engineering. Inverse nodal problem with boundary conditions depending polynomially on the spectral parameter is helpful for studying the problems in mathematics and physics. In this paper, we prove that a dense subset of the nodal set on (0, b) (for any fixed be(1/2,1]) determines the potential on [0,1] and the unknown polynomials of the boundary conditions.