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UNIQUENESS OF THE SOLUTION OF HALF INVERSE PROBLEM FOR THE IMPULSIVE STURM LIOUVILLE OPERATOR
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 Title & Authors
UNIQUENESS OF THE SOLUTION OF HALF INVERSE PROBLEM FOR THE IMPULSIVE STURM LIOUVILLE OPERATOR
Ozkan, A. Sinan; Keskin, Baki; Cakmak, Yasar;
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 Abstract
The half-inverse spectral problem for an impulsive Sturm-Liouville operator consists in reconstruction of this operator from its spectrum and half of the potential. In this study, the spectrum of the impulsive Sturm-Liouville problem is given and by using the Hochstadt and Lieberman`s method we show that if is prescribed on (0, ), then only one spectrum is sufficient to determine on the interval (0, ) for this problem.
 Keywords
Sturm-Liouville operator;determination of the potential;discontinuous condition;half inverse problem;
 Language
English
 Cited by
1.
Inverse spectral problems for the Sturm–Liouville operator with discontinuity, Journal of Differential Equations, 2017, 262, 3, 3093  crossref(new windwow)
 References
1.
P. E. Bulavin and V. M. Kascheev, Solution of the nonhomogeneous heat conduction equation for multilayered bodies, Int. Chem. Engng. 5 (1965), 112-115.

2.
G. Freiling and V. A. Yurko, Inverse Sturm-Liouville Problems and Their Applications, Huntington, NY: Nova Science, 2001.

3.
I. M. Gelfand and B. M. Levitan, On the determination of a differential equation from its spectral function, Amer. Math. Transl. 1 (1951), no. 2, 239-253.

4.
F. Gesztesy and B. Simon, Inverse spectral analysis with partial information on the potential II: The case of discrete spectrum, Trans. Amer. Math. Soc. 352 (2000), no. 6, 2765-2787. crossref(new window)

5.
O. H. Hald, Discontinuous inverse eigenvalue problem, Comm. Pure Appl. Math. 37 (1984), no. 5, 539-577. crossref(new window)

6.
H. Hochstadt and B. Lieberman, An inverse Sturm-Liouville problem with mixed given data, SIAM J. Appl. Math. 34 (1978), no. 4, 676-680. crossref(new window)

7.
O. R. Hryniv and Y. V. Mykytyuk, Half-inverse spectral problems for Sturm-Liouville operators with singular potentials, Inverse Problems 20 (2004), no. 5, 1423-1444. crossref(new window)

8.
B. M. Levitan, and I. S. Sargsyan, Sturm-Liouville and Dirac Operators Kluwer Aca-demic Publishers, Dodrecht/Boston/London, 1991.

9.
M. M. Malamud, Questions of uniqueness in inverse problems for systems of differential equations on a finite interval, Tr. Mosk. Mat. Obs. 60 (1999), 199-258; translation in Trans. Moscow Math. Soc. (1999), 173-224.

10.
V. A. Marchenko, Sturm-Liouville Operators and Their Applications, Birkhauser, 1986.

11.
M. N. Ozisik, Boundary Value Problems of Heat Conduction, Dower, New York, 1989.

12.
L. Sakhnovich, Half inverse problems on the finite interval, Inverse Problems 17 (2001), no. 3, 527-532. crossref(new window)

13.
C.-F. Yang and Z.-Y. Huang, A half-inverse problem with eigenparameter dependent boundary conditions, Numer. Funct. Anal. Optim. 31 (2010), no. 6, 754-762. crossref(new window)

14.
C.-F. Yang, Hochstadt-Lieberman theorem for Dirac operator with eigenparameter de-pendent boundary conditions, Nonlinear Anal. 74 (2011), no. 7, 2475-2484. crossref(new window)

15.
V. F. Zdanovic, V. F., Formulae for the zeros of Dirichlet polynomials and quasi-polynomials, Dokl. Acad. Nauk SSSR 135 (1960), no. 8, 1046-1049.