Spectral properties of an impulsive Sturm-Liouville operator

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Bayram E., Erdal İ., Yardımcı Ş.

JOURNAL OF INEQUALITIES AND APPLICATIONS, vol.2018, 2018 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 2018
  • Publication Date: 2018
  • Doi Number: 10.1186/s13660-018-1781-0
  • Journal Name: JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Impulsive operators, Sturm-Liouville equations, Eigenvalues, Spectral singularities, Scattering function, TRANSMISSION CONDITIONS, DIFFERENCE-EQUATIONS, SINGULARITIES
  • Ankara University Affiliated: Yes

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.