TY  - JOUR
T1  - Existence and Uniqueness of Solutions in Inverse Sturm-Liouville Problems
AU  - Tuz, Münevver
PY  - 2024
DA  - January
Y2  - 2023
JF  - Journal of New Results in Engineering and Natural Sciences
JO  - JRENS
PB  - Tokat Gaziosmanpasa University
WT  - DergiPark
SN  - 2651-4583
SP  - 19
EP  - 26
VL  - 2023
IS  - 19
LA  - en
AB  - In this article, we examined a boundary value problem for the Sturm-Liouville equation defined in the interval [0, L]. The problem with [0, L] corresponds to the small vibrations of a fixed-end straight rope. In these problems, the necessary and sufficient conditions for the unique determination of the potential by only one spectrum at certain parameters of the boundary conditions are investigated. For the inverse problem, it has been examined that the spectrum is effective in describing the potential of the Sturm-Liouville problem alone, thus the intensity of the array. Also, the uniqueness results of this problem are proved using the Leray-Schauder fixed point theorem in a Banach space. Thus, with a different method, an existence and uniqueness result was created for the problem with these boundary conditions.
KW  - Sturm-Liouville problem
KW  - boundary conditions
KW  - Leray–Schauder
KW  - eigenvalue
KW  - spectrum.
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UR  - https://dergipark.org.tr/en/pub/jrens/issue//1209843
L1  - https://dergipark.org.tr/en/download/article-file/2793539
ER  -