On Some Spectral Problems for Sturm–Liouville Equation With Operator Coefficients

Aslanova N., Aslanov K., Kocinac L.

Mathematical Methods in the Applied Sciences, 2025 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Publication Date: 2025
  • Doi Number: 10.1002/mma.10893
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: asymptotics of spectrum, eigenvalue dependent boundary conditions, self-adjoint extensions with exit from space, Sturm–Liouville operator equation
  • Open Archive Collection: Article
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

We offer a detailed treatment of minimal, maximal, dissipative, accumulative, and self-adjoint operator realizations with exit from space of boundary value problem for the Sturm–Liouville equation with unbounded operator coefficient having discrete spectrum and with boundary condition dependent on the Herglotz–Nevanlinna function of eigenparameter. We also study self-adjoint operator realizations having purely discrete spectrum or having continuous spectrum which coincide with any interval on real axis. That is done in terms of boundary conditions. In addition, in particular case, we obtain asymptotics of spectrum of self-adjoint operators with discrete spectrum.