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

Yelda Aygar | Zendy; Elgiz Bairamov | Zendy; Güher Gülçehre Özbey | Zendy

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

Author(s) -

Yelda Aygar,

Elgiz Bairamov,

Güher Gülçehre Özbey

Publication year - 2021

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-2101-45

Subject(s) - mathematics , scattering , mathematical analysis , resolvent , boundary value problem , scattering theory , function (biology) , spectrum (functional analysis) , operator (biology) , sturm–liouville theory , spectral theory of ordinary differential equations , inverse scattering transform , inverse scattering problem , physics , quantum mechanics , banach space , inverse problem , quasinormal operator , biochemistry , chemistry , repressor , evolutionary biology , gene , transcription factor , finite rank operator , biology

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.

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