INVERSE PROBLEMS FOR THE STURM-LIOUVILLE EQUATION WITH THE DISCONTINUOUS COEFFICIENT

被引：3

作者：

Nabiev, Anar Adiloglu ^{[1
]}

Gurdal, Mehmet ^{[2
]}

Saltan, Suna ^{[2
]}

机构：

[1] Cumhuriyet Univ, Fac Sci, Dept Math, TR-58140 Sivas, Turkey

[2] Suleyman Demirel Univ, Fac Sci, Dept Math, TR-32260 Isparta, Turkey

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2017年 / 7卷 / 02期

关键词：

Sturm-Louville equation; boundary value problems; spectral analysis of ordinary differential operators; transformation operator; integral representation; asymptotic formulas for eigenvalues; expansion formula; BOUNDARY-VALUE-PROBLEMS; EIGENVALUE PROBLEMS; SINGULAR POTENTIALS; SPECTRAL PROBLEMS; WAVE SPEED; OPERATORS; INTERVAL; SCATTERING; IMPEDANCE;

D O I：

10.11948/2017035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this study we derive the Gelfand-Levitan-Marchenko type main integral equation of the inverse problem for the boundary value problem L and prove the uniquely solvability of the main integral equation. Further, we give the solution of the inverse problem by the spectral data and by two spectrum.

引用

页码：559 / 580

页数：22

共 44 条

[1]

Akhmedova E. N., 2002, P I MATH MECH NATL A, V16, P208

[2]

Akhmedova E. N., 2010, P SARATOV U MMI, V10, P3

[3] INVERSE WAVE SCATTERING WITH DISCONTINUOUS WAVE SPEED [J].

AKTOSUN, T ;

KLAUS, M ;

VANDERMEE, C .

JOURNAL OF MATHEMATICAL PHYSICS, 1995, 36 (06) :2880-2928

[4] Integral equation methods for the inverse problem with discontinuous wave speed [J].

Aktosun, T ;

Klaus, M ;

vanderMee, C .

JOURNAL OF MATHEMATICAL PHYSICS, 1996, 37 (07) :3218-3245

[5] Inverse Problems for the Quadratic Pencil of the Sturm-Liouville Equations with Impulse [J].

Amirov, Rauf Kh. ;

Nabiev, A. Adiloglu .

ABSTRACT AND APPLIED ANALYSIS, 2013,

[6] On Sturm-Liouville operators with discontinuity conditions inside an interval [J].

Amirov, RK .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 317 (01) :163-176

[7] EFFECT OF DISCONTINUITIES IN DENSITY AND SHEAR VELOCITY ON ASYMPTOTIC OVERTONE STRUCTURE OF TORSIONAL EIGENFREQUENCIES OF EARTH [J].

ANDERSSEN, RS .

GEOPHYSICAL JOURNAL OF THE ROYAL ASTRONOMICAL SOCIETY, 1977, 50 (02) :303-309

[8] INVERSE EIGENVALUE PROBLEMS FOR A STURM-LIOUVILLE EQUATION IN IMPEDANCE FORM [J].

ANDERSSON, LE .

INVERSE PROBLEMS, 1988, 4 (04) :929-971

[9]

[Anonymous], 1977, OPERATORYI SHTURMA L

[10]

[Anonymous], 1963, Differential-Difference Equations

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