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Weyl's type estimates on the eigenvalues of critical Schrödinger operators using improved Hardy–Sobolev inequalities

N B Zographopoulos

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Motivated by the work (Karachalios N I 2008 Lett. Math. Phys. 83 189–99), we present explicit asymptotic estimates on the eigenvalues of the critical Schrödinger operator, involving inverse-square potential, based on improved Hardy–Sobolev-type inequalities.


PACS

02.30.Jr Partial differential equations

02.30.Tb Operator theory

MSC

35J10 Schrödinger operator (See also 35Pxx)

47F05 Partial differential operators (See also 35Pxx, 58Jxx)

35P15 Estimation of eigenvalues, upper and lower bounds

Subjects

Mathematical physics

Dates

Issue 46 (20 November 2009)

Received 16 May 2009, in final form 1 October 2009

Published 22 October 2009



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