ON THE SPECTRUM OF SINGULAR q-STURM-LIOUVILLE OPERATORS ON THE WHOLE AXIS

Allahverdiyev B., Tuna H.

Publications de l'Institut Mathematique, vol.117, no.131, pp.105-114, 2025 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 117 Issue: 131
  • Publication Date: 2025
  • Doi Number: 10.2298/pim2531105a
  • Journal Name: Publications de l'Institut Mathematique
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Central & Eastern European Academic Source (CEEAS), MathSciNet, zbMATH
  • Page Numbers: pp.105-114
  • Keywords: continuous spectrum, discrete spectrum, g-Sturm—Liouville operator, splitting method
  • Open Archive Collection: Article
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

We give some conditions for the self-adjoint operators associated with the g-Sturm—Liouville expressionτy:=−1qDq−1(p(x)Dqy(x))+r(x), −∞<x<∞.to have a discrete spectrum, and investigate the continuous spectra of these operators. We also prove that the regular symmetric g-Sturm—Liouville operator is semi-bounded from below which is not studied in literature yet.