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Inverse nodal problem for polynomial pencil of Sturm‐Liouville operator
Author(s) -
Goktas Sertac,
Koyunbakan Hikmet,
Gulsen Tuba
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5220
Subject(s) - mathematics , sturm–liouville theory , pencil (optics) , eigenfunction , eigenvalues and eigenvectors , operator (biology) , boundary value problem , inverse , mathematical analysis , polynomial , geometry , mechanical engineering , biochemistry , physics , chemistry , repressor , quantum mechanics , transcription factor , engineering , gene
The paper is about boundary value problem for polynomial pencil of Sturm‐Liouville operators. Especially, we find all coefficients of the operator by using nodal points (zeros of eigenfunctions). Regularly, we find eigenvalues, nodal points, and nodal lengths by Prüfer substitution. These results are used to give a reconstruction formula for all complex functions q d ( x ), d = 0 , n − 1 ‾ , which are known potentials in the theory. However, method is similar with some papers; our results more general then because of including many potential functions.