A Study of Scattering Theory of Eigenparameter Dependent Impulsive Sturm-Liouville Equation with Matrix Coefficients
Nonlinear Dynamical Control, Computer Simulation and Optimization Systems: Theory and Applications: Volume 2, World Scientific Publishing , ss.193-205, 2025
- Yayın Türü: Kitapta Bölüm / Araştırma Kitabı
- Basım Tarihi: 2025
- Doi Numarası: 10.1142/9789819815432_0018
- Yayınevi: World Scientific Publishing
- Sayfa Sayıları: ss.193-205
- Ankara Üniversitesi Adresli: Evet
Özet
In this study, we set an eigenparameter dependent impulsive boundary value problem for matrix valued Sturm-Liouville equation on the semi axis. The main purpose of this work is to examine the properties of scattering solutions and scattering function of this problem. Firstly, we obtain Jost solution and Jost function of the operator corresponding to the impulsive boundary value problem. Then, we find scattering function by using Jost function and we investigate scattering function’s properties. We also get resolvent operator, Green function, the sets of eigenvalues and spectral singularities of this problem. Finally, we present an example to demonstrate the application of our results. The novelty in this study is that it is the first study related to the impulsive Sturm-Liouville problem with matrix coefficients whose boundary conditions depend on spectral parameter.