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

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Copy For Citation

Karayel S., Adıgüzelov E.

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

• Publication Type: Article / Article
• Volume: 3
• Publication Date: 2009
• Doi Number: 10.1016/j.cmpb.2012.12.005
• Journal Name: INTERNATIONAL JOURNAL OF MATHEMATICAL ANALYSIS
• Journal Indexes: 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