2022
DOI: 10.35378/gujs.881459
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Spectrum and the Jost Solution of Discrete Impulsive Klein-Gordon Equation with Hyperbolic Eigenparameter

Abstract: Let L denote the quadratic pencil of difference operator with boundary and impulsive conditions generated in l_2 (N) by△(a_(n-1)△y_(n-1) )+(q_n+2λp_n+λ^2 ) y_n=0 , n∈N∖{k-1,k,k+1},y_0=0,(■(y_(k+1)@△y_(k+1) ))=θ(■(y_(k-1)@▽y_(k-1) )); θ=(■(θ_1&θ_2@θ_3&θ_4 )),{θ_i }_(i=1,2,3,4)∈Rwhere {a_n }_( n∈N), {p_n }_( n∈N), {q_n }_( n∈N) are real sequences, λ=2 cosh⁡(z/2) is a hyperbolic eigenparameter and △, ▽ are respectively forward and backward operators. In this paper, the spectral properties of L … Show more

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