scholarly journals Discrete Sturm-Liouville equations with point interaction

2022 ◽  
Author(s):  
Güher Özbey ◽  
yelda AYGAR ◽  
Basak Oznur
Keyword(s):  
Boundary Value Problem ◽  
Discrete Spectrum ◽  
Resolvent Operator ◽  
Boundary Value ◽  
Point Interaction ◽  
Scattering Function ◽  
Asymptotic Equation ◽  
Sturm Liouville

Scattering solutions and several properties of scattering function of a discrete Sturm-Liouville boundary value problem with point interaction (PBVP) are derived. Moreover, resolvent operator, continuous and discrete spectrum of this PBVP are investigated. An asymptotic equation is utilized to get the properties of eigenvalues. An example illustrating the main results is given.

scholarly journals The Levinson-Type Formula for a class of Sturm-Liouville Equation

2021 ◽  
pp. 1219
Author(s):  
Sertac Goktas ◽  
Khanlar R. Mamedov
Keyword(s):  
Boundary Value Problem ◽  
Spectral Parameter ◽  
Liouville Equation ◽  
Boundary Value ◽  
Scattering Data ◽  
Scattering Function ◽  
Type Formula ◽  
Marchenko Equation ◽  
Sturm Liouville

The boundary value problem \[-{\psi}''+q(x)\psi={\lambda}^2 \psi, \quad 0<x<\infty,\] \[{\psi}'(0)-(\alpha_{0}+\alpha_{1}\lambda){\psi}(0)=0 \] is considered, where $\lambda$ is a spectral parameter, $ q(x) $ is real-valued function such that \begin{equation*} \int\limits_{0}^{\infty}(1+x)|q(x)|dx<\infty \end{equation*} with $\alpha_{0}, \alpha_{1}\geq0$ ( $\alpha_{0},\alpha_{1}\in \mathbb{R}$). In this paper, for the above-mentioned boundary value problem, the scattering data is considered and the characteristics properties (such as continuity of the scattering function $ S(\lambda) $ and giving the Levinson-type formula) of this data are studied.{\small \bf Keywords. }{Scattering data, scattering function, Gelfand-Levitan-Marchenko equation, Levinson-type formula.}

scholarly journals Scattering analysis and spectrum of discrete Schrödinger equations with transmission conditions

Filomat ◽  
2017 ◽  
Vol 31 (17) ◽  
pp. 5391-5399 ◽  
Author(s):  
Elgiz Bairamov ◽  
Yelda Aygar ◽  
Dilara Karslıoğlu
Keyword(s):  
Boundary Value Problem ◽  
Discrete Spectrum ◽  
Boundary Value ◽  
Transmission Conditions ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Scattering Function ◽  
Dinger Equation ◽  
Special Case ◽  
Jost Solution

In this paper, we present an investigation about scattering analysis of an transmission boundary value problem (TBVP) which consists a discrete Schr?dinger equation and transmission conditions. Discussing the Jost solution and scattering function of this problem, we find the properties of scattering function of this problem by using the scattering solutions. We also investigate the discrete spectrum of this boundary value problem. Furthermore, we apply the results on an example which is the special case of main TBVP and we discuss the existence of eigenvalues of this example.

scholarly journals Scattering theory of impulsive Sturm-Liouville equations

Filomat ◽  
2017 ◽  
Vol 31 (17) ◽  
pp. 5401-5409 ◽  
Author(s):  
Elgiz Bairamov ◽  
Yelda Aygar ◽  
Basak Eren
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Scattering Theory ◽  
Boundary Value ◽  
Scattering Function ◽  
Jost Function ◽  
Impulsive Boundary Value Problem ◽  
Sturm Liouville ◽  
Jost Solution

In this paper, we investigate scattering theory of the impulsive Sturm-Liouville boundary value problem (ISBVP). In particular, we find the Jost solution and the scattering function of this problem. We also study the properties of the Jost function and the scattering function of this ISBVP. Furthermore, we present two examples by getting Jost function and scattering function of the impulsive boundary value problem. Besides, we examine the eigenvalues of these boundary value problems given in examples in detail.

Factorization Ladders and Eigenfunctions

1949 ◽  
Vol 1 (4) ◽  
pp. 379-396 ◽  
Author(s):  
G. F. D. Duff
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Integral Equations ◽  
Manufacturing Process ◽  
Boundary Value ◽  
Factorization Method ◽  
Sturm Liouville ◽  
The Subject

The eigenfunctions of a boundary value problem are characterized by two quite distinct properties. They are solutions of ordinary differential equations, and they satisfy prescribed boundary conditions. It is a definite advantage to combine these two requirements into a single problem expressed by a unified formula. The use of integral equations is an example in point. The subject of this paper, namely the Schrödinger-Infeld Factorization Method, which is applicable to certain restricted. Sturm-Liouville problems, is based upon another combination of the two properties. The Factorization Method prescribes a manufacturing process.

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