Riv. Mat. Univ. Parma, Vol. 6, No. 2, 2015

Bahram A. Aliev[1], Nargul K. Kurbanova[2] and Yakov Yakubov[3],

Solvability of the abstract Regge boundary value problem and asymptotic behavior of eigenvalues of one abstract spectral problem

Pages: 241-265
Received: 14 August 2014   
Accepted in revised form: 14 January 2015
Mathematics Subject Classification (2010): 47E05, 47A75, 34L15, 34G10, 35J25.
Keywords: Differential-operator equations, elliptic equations, isomorphism, spectral parameter, scattering problem, Regge problem, maximal \(L_p\)-regularity, eigenvalues.
Authors addresses:
[1],[2] : National Academy of Sciences of Azerbaijan, Institute of Mathematics and Mechanics, 9, B. Vahabzade str., Baku 1141, Azerbaijan Republic
[3] : Raymond and Beverly Sackler Faculty of Exact Sciences, School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv 69978, Israel
The third author was supported by the Israel Ministry of Absorption.

Abstract: In the paper, we give an abstract formulation of the classical Regge boundary value problem (but with a constant potential) in a Hilbert space and prove an isomorphism result for the problem. This result implies, in particular, maximal \(L_p\)-regularity for the problem. We also obtain an estimate of the solution with respect to the spectral parameter. Then, for one homogeneous abstract spectral problem, we find asymptotic behavior of its eigenvalues. A possible application of the abstract results to elliptic partial differential equations is shown at the end of the paper.

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