Asymptotic formulas for the number of negative eigenvalues of a differential operator with operator coefficient

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Karayel S., Adıgüzelov E.

INTERNATIONAL JOURNAL OF MATHEMATICAL ANALYSIS, vol.3, pp.491-504, 2009 (Scopus)

  • Publication Type: Article / Article
  • Volume: 3
  • Publication Date: 2009
  • Journal Name: INTERNATIONAL JOURNAL OF MATHEMATICAL ANALYSIS
  • Journal Indexes: Scopus, zbMATH
  • Page Numbers: pp.491-504
  • Yıldız Technical University Affiliated: Yes

Abstract

In this work, we find some asymptotic formulas for the number N(ε) of eigenvalues smaller than −ε (ε > 0) of a self adjoint operator

L which is formed by differential expression (Ly)(x) = −(p(x)y (x)) − Q(x)y(x) and with the boundary condition y(0) = 0 as ε → 0,in

the space L2(0,∞; H )

Mathematics Subject Classification: 47A10, 34L20