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This work develops scattering and spectral analysis of a discrete impulsive Sturm–Liouville equation with spectral parameter in boundary condition. Giving the Jost solution and scattering solutions of this problem, we find scattering function of the problem. Discussing the properties of scattering function, scattering solutions, and asymptotic behavior of the Jost solution, we find the Green function, resolvent operator, continuous and point spectrum of the problem. Finally, we give an example in which the main results are made explicit.

On the spectral and scattering properties of eigenparameter dependent discrete impulsive Sturm–Liouville equations