Results 141 to 150 of about 55,217 (179)
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An inverse nodal problem for integro-differential operators
jiip, 2010Abstract The inverse nodal problem of recovering integral-differential operators with the Sturm–Liouville differential part and the integral part of Volterra type is studied. We reconstruct the potential and the boundary conditions provided the kernel of integral perturbation is known.
Kuryshova, Yulia V., Shieh, Chung-Tsun
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Inverse Nodal Problem for Polynomial Potentials
Numerical Functional Analysis and Optimization, 2021In this work, we study an inverse nodal problem for a differential pencil with boundary condition depends on eigenparameter.
Koyunbakan, Hikmet, Shieh, Chung-Tsun
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Inverse nodal problems on quantum tree graphs
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2021We consider inverse nodal problems for the Sturm–Liouville operators on the tree graphs. Can only dense nodes distinguish the tree graphs? In this paper it is shown that the data of dense-nodes uniquely determines the potential (up to a constant) on the tree graphs. This provides interesting results for an open question implied in the paper.
Yang, Chuan-Fu, Liu, Dai-Quan
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Solution of inverse nodal problems
Inverse Problems, 1989We show that the coefficients in a second-order differential equation can be determined from the positions of the nodes for the eigenfunctions. We prove uniqueness results, derive approximate solutions, give error bounds and present numerical experiments.
Hald, Ole H., McLaughlin, Joyce R.
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Inverse nodal problems for singular problems in the half-line
Boletín de la Sociedad Matemática Mexicana, 2023In this paper, an inverse problem for a singular ordinary differential equation in the half-line is considered. The authors consider a class of positive weights \(\sigma\in L^{1}([0,\infty])\) with \(\int_{0}^{\infty}t\sigma(t ...
Martina Oviedo, Juan Pablo Pinasco
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Approximate solutions of inverse nodal problem with conformable derivative
2023Summary: Our research is about the Sturm-Liouville equation which contains conformable fractional derivatives of order \(\alpha \in (0,1]\) in lieu of the ordinary derivatives. First, we present the eigenvalues, eigenfunctions, and nodal points, and the properties of nodal points are used for the reconstruction of an integral equation.
Akbarpoor, Shahrbanoo, Dabbaghian, Abdol
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The inverse nodal problem for Hill's equation
Inverse Problems, 2006Summary: We study the inverse nodal problem for Hill's equation. In particular, we solve the uniqueness, reconstruction and stability problems using the nodal set of periodic (or anti-periodic) eigenfunctions. Furthermore, we show that the space of periodic potential functions \(q\) normalized by \(\int^{1}_{0} q = 0\) is homeomorphic to the partition ...
Cheng, Y. H., Law, C. K.
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The inverse problem using nodal position data
26th IEEE Conference on Decision and Control, 1987Uniqueness theorems and algorithms are presented for solving inverse problems where the data is nodal positions.
Joyce McLaughlin, Ole Hald
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A uniqueness theorem for inverse nodal problem
Inverse Problems in Science and Engineering, 2007In this article, it is found that the asymptotic formulas for nodal points and nodal length for the differential operators having singularity type at the points 0 and π, it is shown that the potential function can be determined from the positions of the nodes for the eigenfunctions.
Hikmet Koyunbakan, Etibar S. Panakhov
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Examples of Inverse Nodal Problems
1990In this talk we will consider the following problem: What can you say about a vibrating rod, if you know the position of the nodes. A node is a point where an eigenfunction vanishes. We will assume that the mass per unit length is constant and try to determine the elasticity of the rod from the nodes. Instead of presenting general theories, (see [1,2,3]
O. H. Hald, J. R. McLaughlin
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