Expansion of eigenvalues of the perturbed discrete bilaplacian
Expansion of eigenvalues of the perturbed discrete bilaplacian
We consider the family H^μ:=Δ^Δ^-μV^,μ∈R, of discrete Schrödinger-type operators in d-dimensional lattice Zd , where Δ^ is the discrete Laplacian and V^ is of rank-one. We prove that there exist coupling constant thresholds μo,μo≥0 such that for any μ∈[-μo,μo] the discrete spectrum of Hμ^ is empty and for any μ∈R\[-μo,μo] …