Half Inverse Problems for Quadratic Pencils of Sturm-Liouville Operators

Yang, Chuan‐Fu; Zettl, Anton

doi:10.11650/twjm/1500406800

Cited by 25 publications

(17 citation statements)

References 17 publications

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“…In this section, we consider the following half inverse problem by using Hochstadt-Lieberman and Yang-Zettl's methods in [33,40] for problem L. Lemma 3.1. If λ n = λ n for all n ∈ N then β = β.…”

Section: Resultsmentioning

confidence: 99%

Half inverse problem for the impulsive diffusion operator with discontinuous coefficient

Çakmak

Işık

2016

Filomat

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The half inverse problem is to construct coefficients of the operator in a whole interval by using one spectrum and potential known in a semi interval. In this paper, by using the Hocstadt-Lieberman and Yang-Zettl's methods we show that if p (x) and q(x) are known on the interval (π/2, π), then only one spectrum suffices to determine p (x) , q(x) functions and β, h coefficients on the interval (0, π) for impulsive diffusion operator with discontinuous coefficient.

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Section: Resultsmentioning

confidence: 99%

Half inverse problem for the impulsive diffusion operator with discontinuous coefficient

Çakmak

Işık

2016

Filomat

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“…(1.1) with p(x) ∈ W 1 2 (0, 1) and q(x) ∈ L 2 (0, 1) and under (quasi)-periodic boundary conditions or interior given data were considered in [12,14,29]. This kind of problem was considered in various studies (see [1,2,9,[11][12][13][14][15][16][25][26][27]30,32,34,35]). …”

Section: ) {λ N }mentioning

confidence: 99%

On the isospectrality of the scalar energy-dependent Schrödingerproblems

Gulsen¹,

Panakhov²

2018

Turk J Math

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In this study, we discuss the inverse spectral problem for the energy-dependent Schrödinger equation on a finite interval. We construct an isospectrality problem and obtain some relations between constants in boundary conditions of the problems that constitute isospectrality. Above all, we obtain degeneracy of K(x, t) − K0(x, t) and L(x, t) − L0(x, t) by using a different approach. Some of the main results of our study coincide with results reported by Jodeit and Levitan. However, the method to obtain degeneracy is completely different. Furthermore, we consider all above results for the nonisospectral case.

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“…Some aspects of this type problems were studied by many authors (see [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38]). Such problems play an important role in mathematics and have many applications in natural sciences and engineering.…”

Section: Introductionmentioning

confidence: 99%