Expansions of eigenvalues of a discrete bilaplacian with two-dimensional perturbation
https://doi.org/10.26907/0021-3446-2024-10-77-89
Abstract
In this paper we consider the family of operators μH:= ΔΔ— Vμ, μ > 0, that is, a bilaplacian with a finite-dimensional perturbation on a one-dimensional lattice Z , where Δ is a discrete Laplacian, and Vμ is an operator of rank two. It is proved that for any μ > 0 the discrete spectrum μH is two-element e1(μ ) < 0 and e2(μ ) < 0. We find convergent expansions of the eigenvalues ei(μ ), i = 1, 2 in a small neighborhood of zero for small μ > 0.
About the Authors
T. Kh. Rasulov
Bukhara State University
Uzbekistan
Uzbekistan
Tulkin Khusenovich Rasulov
11 M.Ikbol str., Bukhara, 200118
A. M. Khalkhuzhaev
Samarkand State University after named Sharof Rashidov;
V.I. Romanovsky Institute of Mathematics of the Academy of Sciences of Uzbekistan
Uzbekistan
Uzbekistan
Miyassarovich Khalkhuzhaev
15 University blvrd., Samarkand, 140104,
9 University str., Tashkent, 100174
M. A. Pardabaev
Uzbek-Finnish Pedagogical Institute
Uzbekistan
Uzbekistan
Mardon Almuratovich Pardabaev
166 Spitamen str., Samarkand, 140104
Kh. G. Khayitova
Bukhara State University
Uzbekistan
Uzbekistan
Khilola Gafurovna Khayitova
11 M.Ikbol str., Bukhara, 200118
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Review
For citations:
Rasulov T.Kh., Khalkhuzhaev A.M., Pardabaev M.A., Khayitova Kh.G. Expansions of eigenvalues of a discrete bilaplacian with two-dimensional perturbation. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2024;(10):77-89. (In Russ.) https://doi.org/10.26907/0021-3446-2024-10-77-89
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