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- Title
Inverse nodal problem for polynomial pencil of Sturm‐Liouville operator.
- Authors
Goktas, Sertac; Koyunbakan, Hikmet; Gulsen, Tuba
- Abstract
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 qd(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.
- Subjects
INVERSE problems; POLYNOMIAL approximation; NUMERICAL solutions to Sturm-Liouville equations; EXISTENCE theorems; UNIQUENESS (Mathematics)
- Publication
Mathematical Methods in the Applied Sciences, 2018, Vol 41, Issue 17, p7576
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.5220