Abstract and Applied Analysis

Inverse Problems for the Quadratic Pencil of the Sturm-Liouville Equations with Impulse

Rauf Kh. Amırov and A. Adiloglu Nabıev

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Abstract

In this study some inverse problems for a boundary value problem generated with a quadratic pencil of Sturm-Liouville equations with impulse on a finite interval are considered. Some useful integral representations for the linearly independent solutions of a quadratic pencil of Sturm-Liouville equation have been derived and using these, important spectral properties of the boundary value problem are investigated; the asymptotic formulas for eigenvalues, eigenfunctions, and normalizing numbers are obtained. The uniqueness theorems for the inverse problems of reconstruction of the boundary value problem from the Weyl function, from the spectral data, and from two spectra are proved.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 361989, 10 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393443490

Digital Object Identifier
doi:10.1155/2013/361989

Mathematical Reviews number (MathSciNet)
MR3045044

Zentralblatt MATH identifier
1279.34016

Citation

Amırov, Rauf Kh.; Nabıev, A. Adiloglu. Inverse Problems for the Quadratic Pencil of the Sturm-Liouville Equations with Impulse. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 361989, 10 pages. doi:10.1155/2013/361989. https://projecteuclid.org/euclid.aaa/1393443490


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