Inverse problem for a class of Sturm-Liouville operator with spectral parameter in boundary condition

被引：24

作者：

Mamedov, Khanlar R. ^{[1
]}

Cetinkaya, F. Ayca ^{[1
]}

机构：

[1] Mersin Univ, Sci & Letters Fac, Dept Math, TR-33343 Mersin, Turkey

来源：

BOUNDARY VALUE PROBLEMS | 2013年

关键词：

Sturm-Liouville operator; expansion formula; inverse problem; Weyl function; EQUATIONS;

D O I：

10.1186/1687-2770-2013-183

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work aims to examine a Sturm-Liouville operator with a piece-wise continuous coefficient and a spectral parameter in boundary condition. The orthogonality of the eigenfunctions, realness and simplicity of the eigenvalues are investigated. The asymptotic formula of the eigenvalues is found, and the resolvent operator is constructed. It is shown that the eigenfunctions form a complete system and the expansion formula with respect to eigenfunctions is obtained. Also, the evolution of the Weyl solution and Weyl function is discussed. Uniqueness theorems for the solution of the inverse problem with Weyl function and spectral data are proved.

引用

页数：16

共 50 条

[1] Inverse problem for a class of Sturm-Liouville operator with spectral parameter in boundary condition
Khanlar R Mamedov
F Ayca Cetinkaya
Boundary Value Problems, 2013
[2] ON THE INVERSE PROBLEM FOR STURM-LIOUVILLE OPERATOR WITH A NONLINEAR SPECTRAL PARAMETER IN THE BOUNDARY CONDITION
Mamedov, Khanlar R.
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2009, 46 (06) : 1243 - 1254
[3] INVERSE STURM-LIOUVILLE PROBLEM WITH A BOUNDARY CONDITION LINEAR IN THE SPECTRAL PARAMETER
Pivovarchik, Vyacheslav
JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS, 2018,
[4] Inverse scattering problem for Sturm-Liouville operator with nonlinear dependence on the spectral parameter in the boundary condition
Mamedov, Kh. R.
Kosar, Andn. P.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2011, 34 (02) : 231 - 241
[5] Inverse spectral problem for Sturm-Liouville operator with discontinuous coefficient and cubic polynomials of spectral parameter in boundary condition
Col, Aynur
ADVANCES IN DIFFERENCE EQUATIONS, 2015,
[6] Inverse spectral problem for Sturm-Liouville operator with discontinuous coefficient and cubic polynomials of spectral parameter in boundary condition
Aynur Çöl
Advances in Difference Equations, 2015
[7] Uniqueness of the solution to the inverse problem of scattering theory for the Sturm-Liouville operator with a spectral parameter in the boundary condition
Mamedov, KR
MATHEMATICAL NOTES, 2003, 74 (1-2) : 136 - 140
[8] Inverse Sturm-Liouville Problem with Spectral Parameter in the Boundary Conditions
Bondarenko, Natalia P.
Chitorkin, Egor E.
MATHEMATICS, 2023, 11 (05)
[9] Inverse spectral problem for the Sturm-Liouville operator with eigenvalue parameter dependent boundary conditions
Chugunova, MV
OPERATOR THEORY, SYSTEM THEORY AND RELATED TOPICS: THE MOSHE LIVSIC ANNIVERSARY VOLUME, 2001, 123 : 187 - 194
[10] Spectral Problem for the Sturm-Liouville Operator with Retarded Argument Containing a Spectral Parameter in the Boundary Condition
Sen, E.
Acikgoz, M.
Araci, S.
UKRAINIAN MATHEMATICAL JOURNAL, 2017, 68 (08) : 1263 - 1277

← 1 2 3 4 5 →