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

Karayel S. , Adıgüzelov E.

International Journal of Mathematical Analysis, vol.3, pp.491-504, 2009 (Refereed Journals of Other Institutions)

  • Publication Type: Article / Article
  • Volume: 3
  • Publication Date: 2009
  • Doi Number: 10.1016/j.cmpb.2012.12.005
  • Title of Journal : International Journal of Mathematical Analysis
  • Page Numbers: pp.491-504


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