Asymptotic Behaviour of Negative Eigenvalues of an Operator Differential Equation

BAKŞİ Ö.

Filomat, vol.36, no.7, pp.2411-2426, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 7
  • Publication Date: 2022
  • Doi Number: 10.2298/fil2207411b
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.2411-2426
  • Keywords: Hilbert Space, Negative Eigenvalue, Asymptotic Behaviour
  • Yıldız Technical University Affiliated: Yes

Abstract

© 2022, University of Nis. All rights reserved.In this work, we find the asymptotic formulas for the sum of the negative eigenvalues smaller than −ε (ε > 0) of a self-adjoint operator L defined by the following differential expression ℓ(y) = −(p(x)y′ (x))′ − Q(x)y(x) with the boundary condition y(0) = 0 in the space L2 (0, ∞; H).