On Asymptotics of the Sum of the Fourth Power of the Negative Eigenvalues of the Singular Sturm–Liouville Operator

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Bayramov A. M., Bayramoglu M., Kizilbudak S.

Mathematical Methods in the Applied Sciences, vol.48, no.17, pp.16211-16216, 2025 (SCI-Expanded, Scopus) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 17
  • Publication Date: 2025
  • Doi Number: 10.1002/mma.70081
  • 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
  • Page Numbers: pp.16211-16216
  • Keywords: asymptotic formulation, eigenvalues, self-adjoint operator, singular Sturm–Liouville operator
  • Open Archive Collection: AVESIS Open Access Collection
  • Yıldız Technical University Affiliated: Yes

Abstract

In this study, we obtain the asymptotic formula for the sum of fourth power of the negative eigenvalues of the operator (Formula presented.), which we created with the differential expression (Formula presented.) and boundary condition (Formula presented.) in the space (Formula presented.). It is known that the operator (Formula presented.) is self-adjoint, semibounded below, and the negative part of its spectrum is discrete. is self-adjoint, semibounded below, and the negative part of its spectrum is discrete. Additionally, there are some asymptotic formulas for the number of negative eigenvalues of the operator. Our result applies to a class of mathematical physics equations.