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Half‐inverse problems for the quadratic pencil of the Sturm–Liouville equations with impulse
Author(s) -
Amirov Rauf,
Ergun Abdullah,
Durak Sevim
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22559
Subject(s) - sturm–liouville theory , mathematics , eigenvalues and eigenvectors , impulse (physics) , mathematical analysis , quadratic equation , jump , inverse , pencil (optics) , uniqueness , boundary value problem , inverse problem , operator (biology) , geometry , physics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene
In this paper, we consider the inverse spectral problem for the impulsive Sturm–Liouville differential pencils on [0, π ] with the Robin boundary conditions and the jump conditions at the pointπ 2 . We prove that two potentials functions on the whole interval and the parameters in the boundary and jump conditions can be determined from a set of eigenvalues for two cases: (i) the potentials given on0 π 2 . and (ii) the potentials given onπ 2 π , where 0 < α < 1 , respectively. Inverse spectral problems, Sturm–Liouville operator, spectrum, uniqueness.