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 (Peer-Reviewed Journal)


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