Expansions of eigenvalues of a discrete bilaplacian with two-dimensional perturbation
Tulkin H. RasulovBukhara State UniversityA. M. KhalkhuzhaevSamarkand State University after named Sharof Rashidov;
V.I. Romanovsky Institute of Mathematics of the Academy of Sciences of UzbekistanMardon PardabaevUzbek-Finnish Pedagogical InstituteKh. G. KhayitovaBukhara State University
ABI
Аннотация
In this paper we consider the family of operators μ H := ΔΔ — V μ , μ > 0 , that is, a bilaplacian with a finite-dimensional perturbation on a one-dimensional lattice Z , where Δ is a discrete Laplacian, and V μ is an operator of rank two. It is proved that for any μ > 0 the discrete spectrum μ H is two-element e 1 ( μ ) < 0 and e 2 ( μ ) < 0. We find convergent expansions of the eigenvalues e i ( μ ), i = 1 , 2 in a small neighborhood of zero for small μ > 0.
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