Köprübaşi T., Küçükevcİlİoğlu Y.A.Yelda AYGAR KÜÇÜKEVCİLİOĞLU, Turhan KÖPRÜBAŞIKoprubasi, T, Kucukevcilioglu, YA2023-05-092023-05-092022-01-012022-05-012022.01.01Küçükevci̇li̇oğlu, Y., Köprübaşi, T. (2022). Discrete impulsive Sturm–Liouville equation with hyperbolic eigenparameter. Turkish Journal of Mathematics, 46(SI-1), 387-3961300-0098https://search.trdizin.gov.tr/publication/detail/534460/discrete-impulsive-sturm-liouville-equation-with-hyperbolic-eigenparameterhttps://hdl.handle.net/20.500.12597/6304https://hdl.handle.net/20.500.12597/11897Let L denote the selfadjoint diference operator of second order with boundary and impulsive conditions generated in ℓ2 (N) by (equation Presented)where {an}n&i, {bn}„6N are real sequences and A, v are respectively forward and backward operators. In this paper, the spectral properties of L such as the resolvent operator, 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(Equation Presented)Let L denote the selfadjoint difference operator of second order with boundary and impulsive conditions generated in ℓ2 (N) by an−1yn−1 + bnyn + anyn+1 = (2 cosh z) yn , n ∈ N {k − 1, k, k + 1} , y0 = 0 , { yk+1 = θ1yk−1 △yk+1 = θ2 ▽ yk−1 , θ1, θ2 ∈ R, where {an}n∈N , {bn}n∈N are real sequences and △, ▽ are respectively forward and backward operators. In this paper, the spectral properties of L such as the resolvent operator, 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 ∑∞ n=1 n (|1 − an| + |bn|) < ∞.falseinfo:eu-repo/semantics/openAccessDiscrete equations | Eigenvalues | Hyperbolic eigenparameter | Impulsive condition | Resolvent operator | Scattering function | Spectral analysisDiscrete impulsive Sturm–Liouville equation with hyperbolic eigenparameterDiscrete impulsive Sturm–Liouville equation with hyperbolic eigenparameterDiscrete impulsive Sturm-Liouville equation with hyperbolic eigenparameterArticle10.3906/mat-2104-9710.3906/mat-2104-972-s2.0-85126127714WOS:000746268300002534460387387396396461303-6149