Half inverse problems for the singular Sturm-Liouville operator

	Half inverse problems for the singular Sturm-Liouville operator
International Journal of Nonlinear Analysis and Applications
مقاله 253، دوره 13، شماره 2، مهر 2022، صفحه 3161-3171 اصل مقاله (386.56 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.27348.3569
نویسندگان
Rauf Amirov؛ Sevim Durak^*
Sivas Cumhuriyet University, Faculty of Science, Department of Mathematics, 58140, Turkey
چکیده
In this paper, we consider the inverse spectral problem for the impulsive Sturm-Liouville differential pencils on $\left[ 0,\pi\right] $ with the Robin boundary conditions and the jump conditions at the point $\dfrac{\pi}{2}$. 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 are given on $\left(0,\dfrac{\pi}{4}\left( \alpha+\beta\right) \right) .$ (ii) The potentials is given on $\left( \dfrac{\pi}{4}\left( \alpha+\beta\right) ,\dfrac{\pi }{2}\left( \alpha+\beta\right) \right) $, where $0<\alpha<\beta<1$ and $\alpha+\beta>1$, respectively.
کلیدواژه‌ها
Inverse spectral problems؛ Sturm-Liouville Operator؛ spectrum؛ uniqueness
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