Inverse Sturm-Liouville problems with transmission and spectral parameter boundary conditions

Document Type : Research Paper


University of Maragheh


This paper deals with the boundary value problem involving the differential equation

ell y:=-y''+qy=lambda y,

subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions
y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0).

In this problem q(x), d, a , b are real, qin L^2(0,pi), din(0,pi) and lambda is a parameter independent of x. By defining a new Hilbert space and using spectral data of a kind, it is developed the Hochestadt's result based on transformation operator for inverse Sturm-Liouville problem with parameter dependent boundary and discontinuous conditions. Furthermore, it is established a formula for q(x) - tilde{q}(x) in the finite interval, where tilde{q}(x) is an analogous function with q(x).