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The inverse spectral problem for pencils of differential operators

I. M. Guseinov^ab, I. M. Nabiev<sup>ab

a</sup> Baku State University
^b Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences

Abstract: The inverse problem of spectral analysis for a quadratic pencil of Sturm–Liouville operators on a finite interval is considered. A uniqueness theorem is proved, a solution algorithm is presented, and sufficient conditions for the solubility of the inverse problem are obtained.
Bibliography: 31 titles.

UDC: 517.984

MSC: Primary 34B24, 34L05; Secondary 47E05

Received: 11.01.2006 and 11.04.2007

DOI: 10.4213/sm1491

 English version: Sbornik: Mathematics, 2007, 198:11, 1579–1598

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