共查询到20条相似文献,搜索用时 0 毫秒
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We study non-self-adjoint second-order differential operators with a constant delay. We establish properties of the spectral characteristics and investigate the inverse problem of recovering operators from their spectra. The uniqueness theorem is proved for this inverse problem. 相似文献
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Turhan Koprubasi Ram N. Mohapatra 《Mathematical Methods in the Applied Sciences》2023,46(2):1466-1478
In this paper, an inverse scattering problem for discrete Sturm–Liouville equation with eigenparameter-dependent boundary condition is investigated. In quest of finding scattering function and the main equation of this problem, the uniqueness of the kernel is proven. Also, an appropriate Levinson-type formula based on the continuity of scattering function is given. 相似文献
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Yongxia Guo 《Applicable analysis》2013,92(5):1025-1031
The uniqueness problem of inverse Sturm–Liouville problems with the potential known on an interior subinterval is considered. We prove that the potential on the entire interval and boundary conditions are uniquely determined in terms of the known eigenvalues and some information on the eigenfunctions at some interior point (interior spectral data). Moreover, we also concern with the situation where the potential q is C2k-smoothness at some given points. 相似文献
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Mathematical Notes - The existence of real solutions of a nonlinear equation in a neighborhood of an abnormal (degenerate) point is studied. We prove that if the mapping describing this equation... 相似文献
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In this article we obtain the sharp asymptotic formulas for the eigenvalues and eigenfunctions of the non-self-adjoint operators generated by a system of the Sturm–Liouville equations with Dirichlet and Neumann boundary conditions. Using these asymptotic formulas, we find a condition on the potential for which the root functions of these operators form a Riesz basis. 相似文献
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We use the variational method to establish criteria for the existence of conjugate points and for the oscillation property of the linear differential Sturm–Liouville equation. 相似文献
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《Journal of Computational and Applied Mathematics》2001,132(2):443-459
The numerical solution of the Sturm–Liouville problem can be achieved using shooting to obtain an eigenvalue approximation as a solution of a suitable nonlinear equation and then computing the corresponding eigenfunction. In this paper we use the shooting method both for eigenvalues and eigenfunctions. In integrating the corresponding initial value problems we resort to the boundary value method. The technique proposed seems to be well suited to supplying a general formula for the global discretization error of the eigenfunctions depending on the discretization errors arising from the numerical integration of the initial value problems. A technique to estimate the eigenvalue errors is also suggested, and seems to be particularly effective for the higher-index eigenvalues. Numerical experiments on some classical Sturm–Liouville problems are presented. 相似文献
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Mathematical Notes - 相似文献
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Mohammad Shahriari Aliasghar Jodayree Akbarfam Gerald Teschl 《Journal of Mathematical Analysis and Applications》2012,395(1):19-29
We establish various uniqueness results for inverse spectral problems of Sturm–Liouville operators with a finite number of discontinuities at interior points at which we impose the usual transmission conditions. We consider both the cases of classical Robin and of eigenparameter dependent boundary conditions. 相似文献
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Two inverse problems for the Sturm-Liouville operator Ly = s-y″ + q(x)y on the interval [0, fy] are studied. For θ ⩾ 0, there is a mapping F:W
2θ → l
B
θ, F(σ) = {s
k
}1∞, related to the first of these problems, where W
2∞ = W
2∞[0, π] is the Sobolev space, σ = ∫ q is a primitive of the potential q, and l
B
θ is a specially constructed finite-dimensional extension of the weighted space l
2θ, where we place the regularized spectral data s = {s
k
}1∞ in the problem of reconstruction from two spectra. The main result is uniform lower and upper bounds for ∥σ - σ1∥θ via the l
B
θ-norm ∥s − s1∥θ of the difference of regularized spectral data. A similar result is obtained for the second inverse problem, that is, the
problem of reconstructing the potential from the spectral function of the operator L generated by the Dirichlet boundary conditions. The result is new even for the classical case q ∈ L
2, which corresponds to θ = 1. 相似文献
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Mathematical Notes - The matrix Sturm–Liouville operator on a finite interval with boundary conditions in general self-adjoint form and with singular potential of class $$W_2^{-1}$$ is... 相似文献
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Jesús Rodríguez Zachary Abernathy 《Journal of Difference Equations and Applications》2013,19(3):431-445
This paper is devoted to the study of nonlinear difference equations subject to global nonlinear boundary conditions. We provide sufficient conditions for the existence of solutions based on properties of the nonlinearities and the eigenvalues of an associated linear Sturm–Liouville problem. 相似文献