Spectrum and the Jost Solution of Discrete Impulsive Klein-Gordon Equation with Hyperbolic Eigenparameter

Abstract

Let ʟ denote the quadratic pencil of difference operator with boundary and impulsive conditions generated in ℓ2(ℕ) by (Formula Presented) are real sequences, λ = 2 cosh (Formula Presented) is a hyperbolic eigenparameter and △, ▽ are respectively forward and backward operators. In this paper, the spectral properties of ʟ such as the spectrum, the eigenvalues, the scattering function and their properties are investigated. Moreover, an example about the scattering function and the existence of eigenvalues is given in the special cases, if (Formula Presented).