University of Tabriz Computational Methods for Differential Equations 2345-3982 2 3 2014 07 01 Inverse Sturm-Liouville problems with transmission and spectral parameter boundary conditions 123 139 3006 EN Mohammad Shahriari University of Maragheh Journal Article 2014 02 22 This paper deals with the boundary value problem involving the differential equation <br /> <br /> ell y:=-y''+qy=lambda y, <br /> <br /> subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions <br /> y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). <br /> <br />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). https://cmde.tabrizu.ac.ir/article_3006_b58f6612cd4666d0abfa3f6283667255.pdf