scholarly journals Scattering Function and The Resolvent of The Impulsive Boundary Value Problem

2020 ◽  
pp. 1-1
Author(s):  
Elgiz BAYRAM ◽  
Güler Başak ÖZNUR
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Scattering Function ◽  
Impulsive Boundary Value Problem

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.

scholarly journals On a class of second-order impulsive boundary value problem at resonance

2006 ◽  
Vol 2006 ◽  
pp. 1-11
Author(s):  
Guolan Cai ◽  
Zengji Du ◽  
Weigao Ge
Keyword(s):  
Boundary Value Problem ◽  
Existence Result ◽  
Boundary Value ◽  
General Theorem ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Point Boundary ◽  
At Resonance ◽  
Impulsive Boundary Value Problem ◽  
Problem At Resonance

We consider the following impulsive boundary value problem,x″(t)=f(t,x,x′),t∈J\{t1,t2,…,tk},Δx(ti)=Ii(x(ti),x′(ti)),Δx′(ti)=Ji(x(ti),x′(ti)),i=1,2,…,k,x(0)=(0),x′(1)=∑j=1m−2αjx′(ηj). By using the coincidence degree theory, a general theorem concerning the problem is given. Moreover, we get a concrete existence result which can be applied more conveniently than recent results. Our results extend some work concerning the usualm-point boundary value problem at resonance without impulses.

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 On Impulsive Boundary Value Problem with Riemann-Liouville Fractional Order Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Zareen A. Khan ◽  
Rozi Gul ◽  
Kamal Shah
Keyword(s):  
Boundary Value Problem ◽  
Fractional Order ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Order Derivative ◽  
Liouville Type ◽  
Fractional Order Derivative ◽  
Impulsive Boundary Value Problems ◽  
Impulsive Boundary Value Problem ◽  
The Subject

Our manuscript is devoted to investigating a class of impulsive boundary value problems under the concept of the Riemann-Liouville fractional order derivative. The subject problem is of implicit type. We develop some adequate conditions for the existence and puniness of a solution to the proposed problem. For our required results, we utilize the classical fixed point theorems from Banach and Scheafer. It is to be noted that the impulsive boundary value problem under the fractional order derivative of the Riemann-Liouville type has been very rarely considered in literature. Finally, to demonstrate the obtained results, we provide some pertinent examples.

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.}

Sign in / Sign up

Export Citation Format

Share Document