ON THE ASYMPTOTIC BEHAVIOUR OF THE UNSTABLE BLOCH EIGENVALUES OF A POLYHARMONIC MATRIX OPERATOR

Karakılıç S., Özcan S., Akduman S.

REPORTS ON MATHEMATICAL PHYSICS, vol.96, pp.100-120, 2025 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 96
  • Publication Date: 2025
  • Journal Name: REPORTS ON MATHEMATICAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.100-120
  • Dokuz Eylül University Affiliated: Yes

Abstract

We explore the asymptotic behaviour of the so-called unstable Bloch eigenvalues

of the Polyharmonic matrix operator (−Δ)l + V (x) with 1

2 < l < 1, in the single

resonance domain which is a subset of resonance domain – the set of eigenvalues situated

close to the diffraction hyperplanes. The single resonance domain approaches

full measure asymptotically across the entire resonance domain. In our analysis, we

discover a significant trend: as energy levels increase, the eigenvalues are related to

those of a Sturm-Liouville operator.