AN INVERSE PROBLEM FOR THE SECOND-ORDER INTEGRO-DIFFERENTIAL PENCIL

被引：3

作者：

Bondarenko, Natalia Pavlovna ^{[1
,2
]}

机构：

[1] Samara Natl Res Univ, Dept Appl Math & Phys, Moskovskoye Shosse 34, Samara 443086, Russia

[2] Saratov NG Chernyshevskii State Univ, Dept Mech & Math, Astrakhanskaya 83, Saratov 410012, Russia

来源：

TAMKANG JOURNAL OF MATHEMATICS | 2019年 / 50卷 / 03期

基金：

俄罗斯科学基金会;

关键词：

Inverse spectral problem; Sturm-Liouville integro-differential pencil; polynomial dependence on the spectral parameter; eigenparameter-dependent boundary condition; SPECTRAL PROBLEM; OPERATOR;

D O I：

10.5556/j.tkjm.50.2019.3348

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the second-order (Sturm-Liouville) integro-differential pencil with polynomial dependence on the spectral parameter in a boundary condition. The inverse problem is solved, which consists in reconstruction of the convolution kernel and one of the polynomials in the boundary condition by using the eigenvalues and the two other polynomials. We prove uniqueness of solution, develop a constructive algorithm for solving the inverse problem, and obtain necessary and sufficient conditions for its solvability.

引用

页码：223 / 231

页数：9

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