Inverse problem for interior spectral data of the Sturm – Liouville operator

Mochizuki, Kiyoshi; Trooshin, Igor

doi:10.1515/jiip.2001.9.4.425

Cited by 52 publications

(38 citation statements)

References 5 publications

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“…The aim of this paper is to give two uniqueness theorems from some eigenvalues and information on eigenfunctions at some an internal point in the interval [0, π]. Note that the results obtained are new and natural generalizations of the well-known one for the classical Sturm-Liouville operators which were studied in [24], for a special case that p(x) ≡ 0 and the parameters h and H are fixed in Eq. (1.1).…”

Section: Introductionmentioning

confidence: 87%

Determination of a differential pencil from interior spectral data

Yang

Guo

2011

Journal of Mathematical Analysis and Applications

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In this paper, inverse spectra problems for a differential pencil are studied. By using the approach similar to those in Hochstadt and Lieberman (1978) [14] and Ramm (2000) [26], we prove that (1) if p(x) (or q(x)) is full given on the interval [0, π ], then a set of values of eigenfunctions at the mid-point of the interval [0, π ] and one spectrum suffice to determine q(x) (or p(x)) on the interval [0, π ] and all parameters in the boundary conditions; (2) if p(x) (or q(x)) is full given on the interval [0, π ], then some information on eigenfunctions at some internal point b ∈ ( π 2 , π ) and parts of two spectra suffice to determine q(x) (or p(x)) on the interval [0, π ] and all parameters in the boundary conditions.

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Section: Introductionmentioning

confidence: 87%

Determination of a differential pencil from interior spectral data

Yang

Guo

2011

Journal of Mathematical Analysis and Applications

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“…For the problem B without discontinuous conditions, i.e., in the case where a 1 = 1 and a 2 = 0 for the conditions (1.3), Theorem 2.1 was already proved in [26].…”

Section: Resultsmentioning

confidence: 94%

An Interior Inverse Problem for Discontinuous Boundary-Value Problems

Yang

2009

Integr. equ. oper. theory

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“…may be called the interior spectral data associated with the problem (1.1)-(1.2) in light of [17] and [22] .…”

Section: Corollary 25: Under the Assumption Of Theorem 22 Withmentioning

confidence: 99%

Determination of differential pencils from dense nodal subset in an interior subinterval

Guo

Wei

2014

Isr. J. Math.

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The uniqueness problem of the inverse nodal problem for the differential pencils defined on interval [0, 1] with the Dirichlet boundary conditions is considered. We prove that a bilaterally dense subset of the nodal set in interior subinterval (a 1 , a 2 )(⊂ [0, 1]) can determine the pencil uniquely. However, in the case of 1/2 / ∈ [a 1 , a 2 ] we need additional spectral information to treat this problem, which is associated with the derivatives of eigenfunctions at some known nodal points.

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Inverse problem for interior spectral data of the Sturm – Liouville operator

Cited by 52 publications

References 5 publications

Determination of a differential pencil from interior spectral data

Determination of a differential pencil from interior spectral data

An Interior Inverse Problem for Discontinuous Boundary-Value Problems

Determination of differential pencils from dense nodal subset in an interior subinterval

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