@article {
author = {Shahriari, Mohammad and Jodayree Akbarfam, Aliasghar},
title = {Inverse Sturm-Liouville problem with discontinuity conditions},
journal = {Sahand Communications in Mathematical Analysis},
volume = {01},
number = {1},
pages = {29-40},
year = {2014},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {},
abstract = {This paper deals with the boundary value problem involving the differential equation \begin{equation*} \ell y:=-y''+qy=\lambda y, \end{equation*} subject to the standard boundary conditions along with the following discontinuity conditions at a point $a\in (0,\pi)$ \begin{equation*} y(a+0)=a_1 y(a-0),\quad y'(a+0)=a_1^{-1}y'(a-0)+a_2 y(a-0), \end{equation*} where $q(x), \ a_1 ,\ a_2$ are real, $q\in L^{2}(0,\pi)$ and $\lambda$ is a parameter independent of $x$. We develop the Hochestadt's result based on the transformation operator for inverse Sturm-Liouville problem when there are discontinuous conditions. Furthermore, we establish a formula for $q(x) - \tilde{q}(x)$ in the finite interval where $q(x)$ and $\tilde{q}(x)$ are analogous functions.},
keywords = {Inverse problem,Sturm-Liouville problems,Discontinuous conditions,Green's function},
url = {https://scma.maragheh.ac.ir/article_11264.html},
eprint = {https://scma.maragheh.ac.ir/article_11264_f018e30effb001af0711f93b3ef19f83.pdf}
}