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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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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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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 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 problems for singular diffusion equation
Mathematical Methods in the Applied SciencesIn this study, some properties of the pencils of singular Sturm–Liouville operators are investigated. Firstly, the behaviors of eigenvalues and eigenfunctions is learned, then for each discontinuity point a solution of the inverse problem is given to determine the potential function and parameters , and with the help of a dense set of nodes.
Rauf Amirov, Sevim Durak
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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 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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Inverse nodal problem for singular differential operators
Journal of Inverse and Ill-posed Problems, 2005The inverse nodal problem is solved for the boundary value problem \[ -y''+\left(\frac{\nu-1/4}{x^2}+q(x)\right)y=\lambda y,\;\;\nu>0 ...
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