The cubic eigenparameter dependent discrete Dirac equations with principal functions
Pages : 1742-1760
View : 12 | Download : 7
Publication Date : 2019-08-01
Article Type : Research Paper
Abstract :Let us consider the Boundary Value Problem insert ignore into journalissuearticles values(BVP); for the discrete Dirac Equations {
┊ #0.1
a_{n+1}y_{n+1}⁽²⁾+b_{n}y_{n}⁽²⁾+p_{n}y_{n}⁽¹⁾=λy_{n}⁽¹⁾ a_{n-1}y_{n-1}⁽¹⁾+b_{n}y_{n}⁽¹⁾+q_{n}y_{n}⁽²⁾=λy_{n}⁽²⁾ , n∈ℕ, insert ignore into journalissuearticles values(γ₀+γ₁λ+γ₂λ²+γ₃λ³);y₁⁽²⁾+insert ignore into journalissuearticles values(β₀+β₁λ+β₂λ²+β₃λ³);y₀⁽¹⁾=0, #0.2 where insert ignore into journalissuearticles values(a_{n});, insert ignore into journalissuearticles values(b_{n});, insert ignore into journalissuearticles values(p_{n}); and insert ignore into journalissuearticles values(q_{n});, n∈ℕ are complex sequences, γ_{i}, β_{i}∈ℂ, i=0,1,2 and λ is a eigenparameter. Discussing the eigenvalues and the spectral singularities, we prove that the BVP insert ignore into journalissuearticles values(0.1);, insert ignore into journalissuearticles values(0.2); has a finite number of eigenvalues and spectral singularities with a finite multiplicities, if ∑_{n=1}^{∞}expinsert ignore into journalissuearticles values(εn^{δ});insert ignore into journalissuearticles values(|1-a_{n}|+|1+b_{n}|+|p_{n}|+|q_{n}|);<∞, holds, for some ε>0 and insert ignore into journalissuearticles values(1/2);≤δ≤1.
Keywords : Discrete Dirac equations, Eigenparameter, Spectral analysis, Spectrum, Principal functions
