ASYMPTOTICS OF EIGENVALUES OF RANK-ONE PERTURBATIONS OF THE DISCRETE SCHRÖDINGER OPERATOR ON TWO-DIMENSIONAL LATTICE - Almuratov Firdavsjon; Pardabaev Mardon; Bobonazarova Aynura, (FAN VA TA'LIM INTEGRATSIYASI (INTEGRATION OF SCIENCE AND EDUCATION), 2024)
We consider the family of discrete Schrödinger-type operator in two-dimensional lattice . We establish the existence or non-existence and also the finiteness of eigenvalues of lying above the essential spectrum. Moreover, we study the properties of eigenvalues as a function of in particular, we find the asymptotics of eigenvalues as sufficiently small and positive