Results 101 to 110 of about 142 (134)
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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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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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A solution of the inverse nodal problem
Inverse Problems, 1997The author considers the Sturm-Liouville problem \[ - y''+q(x)y=\lambda y, \qquad y(0)\cos\alpha+ y'(0)\sin\alpha=0, \quad y(1)\cos\beta+ y'(1)\sin\beta=0 \] and demonstrates how the potential function \(q(x)\) can be determined from observable eigenfunction nodes when either \(\alpha\) or \(\beta=0\) but not both. This extends work by \textit{O.
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Incomplete Inverse Spectral and Nodal Problems for Differential Pencils
Results in Mathematics, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Buterin, S. A., Shieh, C.-T.
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The sharp conditions of the uniqueness for inverse nodal problems
Journal of Differential Equations, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yongxia Guo, Guangsheng Wei
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The inverse nodal problem on the smoothness of the potential function
Inverse Problems, 1999The authors correct the lemma 2.2 in the paper by \textit{Y. H. Cheng}, \textit{C. K. Law} and \textit{J. Tsay} [J. Math. Anal. Appl. 248, 145--155 (2000; Zbl 0960.34018)]. Fortunately, the mistakes do not affect the validity of the results in the paper mentioned before.
Law, C. K. +2 more
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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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INVERSE NODAL PROBLEM FOR THE INTEGRODIFFERENTIAL DIRAC OPERATOR WITH A DELAY IN THE KERNEL
Journal of Integral Equations and Applications, 2022The author analyzes an inverse nodal problem for an integro-differential Dirac system with an integral delay on a finite interval. A uniqueness result is obtained for the solution of this problem, and a constructive procedure is proposed to solve it.
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Inverse problems for the boundary value problem with the interior nodal subsets
Applicable Analysis, 2016In this paper, inverse nodal problems for Sturm–Liouville equations with boundary conditions polynomially dependent on the spectral parameter were studied. The authors showed that some uniqueness theorems on the potential function hold by the Weyl function, respectively.
Wang, Yu Ping +2 more
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Inverse nodal problem for p–laplacian dirac system
Mathematical Methods in the Applied Sciences, 2016In this study, we solve an inverse nodal problem for p‐Laplacian Dirac system with boundary conditions depending on spectral parameter. Asymptotic formulas of eigenvalues, nodal points and nodal lengths are obtained by using modified Prüfer substitution.
Gulsen, Tuba +2 more
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