Determination of a differential operator with discontinuity from interior spectral data

Neamaty, A.; Khalili, Yasser

doi:10.1080/17415977.2013.848436

Cited by 10 publications

(2 citation statements)

References 15 publications

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“…They proved that the spectrum of the problem −y + q(x)y = λy, t ∈ (0, 1) y (0) − hy(0) = y (1) + Hy(1) = 0 and the logarithmic derivatives of the eigenfunctions at the point 1/2 uniquely determine the potential q(x) on the whole interval [0, 1] almost everywhere. This kind of problems for the differential operators on a continuous interval were studied in [8]- [14], [18,22,23], [28]- [34].…”

Section: Introductionmentioning

confidence: 99%

Determination of a differential pencil from interior spectral data on a union of two closed intervals

2021

Turk J Math

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Section: Introductionmentioning

confidence: 99%

Determination of a differential pencil from interior spectral data on a union of two closed intervals

2021

Turk J Math

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“…Mochizuki and Trooshin [20] showed that the spectral data of parts of two spectra and a set of values of eigenfunctions at some internal point suffice to determine the potential, and they addressed the interior inverse problem of Sturm-Liouville operators on the finite interval [0,1]. Afterwards, this technique has been used by some authors to survey the inverse problem of Sturm-Liouville operators in various forms [10,22,25,29,33]. Alongside this method, in [9], Hochstadt and Lieberman found the half inverse problem method and showed that if the potential is prescribed on [1/2, 1], one spectrum can uniquely determine the potential on the whole interval [0, 1].…”

Section: Introductionmentioning

confidence: 99%

Recovering differential pencils with spectral boundary conditions and spectral jump conditions

Khalili

Băleanu

2020

J Inequal Appl

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In this work, we discuss the inverse problem for second order differential pencils with boundary and jump conditions dependent on the spectral parameter. We establish the following uniqueness theorems: $(i)$ ( i ) the potentials $q_{k}(x)$ q k ( x ) and boundary conditions of such a problem can be uniquely established by some information on eigenfunctions at some internal point $b\in (\frac{\pi }{2},\pi )$ b ∈ ( π 2 , π ) and parts of two spectra; $(ii)$ ( i i ) if one boundary condition and the potentials $q_{k}(x)$ q k ( x ) are prescribed on the interval $[\pi /2(1-\alpha ),\pi ]$ [ π / 2 ( 1 − α ) , π ] for some $\alpha \in (0, 1)$ α ∈ ( 0 , 1 ) , then parts of spectra $S\subseteq \sigma (L)$ S ⊆ σ ( L ) are enough to determine the potentials $q_{k}(x)$ q k ( x ) on the whole interval $[0, \pi ]$ [ 0 , π ] and another boundary condition.

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On the determination of the impulsive Sturm–Liouville operator with the eigenparameter‐dependent boundary conditions

Khalili

Kadkhoda²,

Băleanu

2020

Math Methods in App Sciences

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In the present work, we consider the inverse problem for the impulsive Sturm–Liouville equations with eigenparameter‐dependent boundary conditions on the whole interval (0,π) from interior spectral data. We prove two uniqueness theorems on the potential q(x) and boundary conditions for the interior inverse problem, and using the Weyl function technique, we show that if coefficients of the first boundary condition, that is, h1,h2, are known, then the potential function q(x) and coefficients of the second boundary condition, that is, H1,H2, are uniquely determined by information about the eigenfunctions at the midpoint of the interval and one spectrum or partial information on the eigenfunctions at some internal points and some of two spectra.

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Determination of a differential operator with discontinuity from interior spectral data

Cited by 10 publications

References 15 publications

Determination of a differential pencil from interior spectral data on a union of two closed intervals

Determination of a differential pencil from interior spectral data on a union of two closed intervals

Recovering differential pencils with spectral boundary conditions and spectral jump conditions

On the determination of the impulsive Sturm–Liouville operator with the eigenparameter‐dependent boundary conditions

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