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Incomplete inverse problems for the Sturm-Liouville type differential equation with the spectral boundary condition | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 9، دوره 16، شماره 4، تیر 2025، صفحه 103-108 اصل مقاله (365.56 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.32952.4900 | ||
| نویسندگان | ||
| Yasser Khalili* 1؛ Nematollah Kadkhoda2 | ||
| 1Department of Basic Sciences, Sari Agricultural Sciences and Natural Resources University, 578 Sari, Iran | ||
| 2Department of Mathematics, Faculty of Engineering Science, Quchan University of Technology, Quchan, Iran | ||
| تاریخ دریافت: 20 دی 1402، تاریخ پذیرش: 22 اسفند 1402 | ||
| چکیده | ||
| In this study, we examine the inverse problem for the differential equation of the Sturm-Liouville type with the spectral boundary condition in the finite interval. Using Lieberman-Hochstadt's method, we show that if $p(x)$ is prescribed on the half interval $\left(\frac{\pi}{2},\pi\right)$ then a single spectrum suffices to determine $p(x)$ on $(0,\pi)$. Moreover, applying Gesztesy-Simon's method, we demonstrate that if $p(x)$ is assumed over the given segment $[\pi/2(1 - \theta), \pi]$ where $\theta \in (0, 1),$ a finite number of the spectrum is enough to give $p(x)$ on $(0, \pi)$. | ||
| کلیدواژه‌ها | ||
| Sturm-Liouville equation؛ Inverse problem؛ Spectrum | ||
| مراجع | ||
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