Spectrum of the quadratic eigenparameter dependent discrete Dirac equations

Abstract

Let us consider the Boundary Value Problem (BVP) for the discrete Dirac equations {equation presented}, where (an), (bn), (p n) and (qn), n ∈ N are complex sequences, γi,βi ∈ C, i = 0, 1, 2, and λ is an eigenparameter. Discussing the eigenvalues and the spectral singularities, we prove that this BVP has a finite number of eigenvalues and spectral singularities with a finite number of multiplicities, if {equation presented}, holds, for some ε > 0 and 1/2 ≤ δ ≤ 1. ©2014 Koprubasi; licensee Springer.