%0 Journal Article
%T Inverse Sturm-Liouville problems with transmission and spectral parameter boundary conditions
%J Computational Methods for Differential Equations
%I University of Tabriz
%Z 2345-3982
%A Shahriari, Mohammad
%D 2014
%\ 07/01/2014
%V 2
%N 3
%P 123-139
%! Inverse Sturm-Liouville problems with transmission and spectral parameter boundary conditions
%K Inverse Sturm-Liouville problem
%K Jump conditions
%K Green's function
%K Eigenparameter dependent condition
%K Transformation operator
%R
%X 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).
%U https://cmde.tabrizu.ac.ir/article_3006_b58f6612cd4666d0abfa3f6283667255.pdf