Spectral properties of an impulsive Sturm–Liouville operator

Abstract

This work is devoted to discuss some spectral properties and the scattering function of the impulsive operator generated by the Sturm–Liouville equation. We present a different method to investigate the spectral singularities and eigenvalues of the mentioned operator. We also obtain the finiteness of eigenvalues and spectral singularities with finite multiplicities under some certain conditions. Finally, we illustrate our results by a detailed example.

Scattering theory of quadratic eigenparameter depending impulsive Sturm-Liouville equations

“…Impulsive condition is well developed in case of continuity. The scattering analysis of the impulsive Sturm-Liouville equation was examined in the studies of Bairamov et al [3,5,6]. The difference in our study is that the spectral parameter ζ exists both in differential equation and in boundary condition.…”

Scattering properties of the nonlinear eigenvalue‐dependent Sturm‐Liouville equations with sign‐alternating weight and jump condition

“…The matrix B is called transfer matrix of the impulsive Sturm-Liouville equation. (2.4) is called the jump condition [17,26,28]. We presume that the real valued potential q (x) holds…”

Negatif Yoğunluk Fonksiyonuna Sahip Kendine Eşlenik Olmayan Schrödinger Operatörü Üzerine Bir Çalışma

“…Similarly, the representation of the main equation has been affected by the discontinuous weight, too. As a consequence, discontinuous positive valued weight function case took a prominent attention from various authors (Darwish, 1993;Gasymov & El-Reheem, 1993;Guseinov & Pashaev, 2002;Adıvar & Akbulut, 2010;Mamedov & Cetinkaya, 2015;Nabiev & Mamedov, 2015;Bairamov et. al., 2018).…”