×

A stability result for an inverse problem with integrodifferential operator on a finite interval. (English) Zbl 1464.45027

Summary: A boundary value problem consisting of an integrodifferential equation, together with boundary conditions dependent on the spectral parameter, is investigated. The asymptotic behavior of the eigenvalues is studied, and we prove the uniqueness and the stability theorems for the solution of the inverse problem.

MSC:

45Q05 Inverse problems for integral equations
45C05 Eigenvalue problems for integral equations
45M10 Stability theory for integral equations
PDFBibTeX XMLCite
Full Text: DOI Euclid

References:

[1] S. A. Buterin, “On an inverse spectral problem for a convolution integro-differential operator”, Results Math. 50:3-4 (2007), 173-181. · Zbl 1135.45007
[2] S. A. Buterin, “On inverse spectral problem for non-selfadjoint Sturm-Liouville operator on a finite interval”, J. Math. Anal. Appl. 335:1 (2007), 739-749. · Zbl 1132.34010
[3] J. B. Conway, Functions of one complex variable, I, Graduate Texts in Mathematics 158, Springer, 1995.
[4] A. Dabbaghian, S. Akbarpour, and A. Neamaty, “The uniqueness theorem for discontinuous boundary value problems with aftereffect using the nodal points”, Iran. J. Sci. Technol. Trans. A Sci. 36:3 (2012), 391-394. · Zbl 1267.34135
[5] G. Freiling and V. Yurko, Inverse Sturm-Liouville problems and their applications, Nova Science, Huntington, NY, 2001. · Zbl 1037.34005
[6] F. Gesztesy and B. Simon, “On local Borg-Marchenko uniqueness results”, Comm. Math. Phys. 211:2 (2000), 273-287. · Zbl 0985.34077
[7] R. O. Hryniv and Y. V. Mykytyuk, “Half-inverse spectral problems for Sturm-Liouville operators with singular potentials”, Inverse Problems 20:5 (2004), 1423-1444. · Zbl 1074.34007
[8] H. Koyunbakan, “The inverse nodal problem for a differential operator with an eigenvalue in the boundary condition”, Appl. Math. Lett. 21:12 (2008), 1301-1305. · Zbl 1195.34021
[9] E. Kreyszig, Introductory functional analysis with applications, Wiley, New York, 1978. · Zbl 0368.46014
[10] Y. V. Kuryshova, “The inverse spectral problem for integrodifferential operators”, Mat. Zametki 81:6 (2007), 855-866. In Russian; translated in Math. Notes. 81 (2007), 767-777. · Zbl 1142.45006
[11] B. J. Levin, Distribution of zeros of entire functions, American Mathematical Society, 1964. · Zbl 0152.06703
[12] B. M. Levitan, “The application of generalized displacement operators to linear differential equations of the second order”, Uspehi Matem. Nauk \((\) N.S.\() 4\):1 (1949), 3-112. In Russian.
[13] V. A. Marchenko and K. V. Maslov, “Stability of the problem of the reconstruction of the Sturm-Liouville operator in terms of the spectral function”, Mat. Sb. \((\) N.S.\() 81\):4 (1970), 525-551. In Russian; translated in Math. USSR Sbornik 10:4 (1970), 475-502. · Zbl 0216.17102
[14] J. R. McLaughlin, “On uniqueness theorems for second order inverse eigenvalue problems”, J. Math. Anal. Appl. 118:1 (1986), 38-41. · Zbl 0592.34013
[15] S. Mosazadeh, “The stability of the solution of an inverse spectral problem with a singularity”, Bull. Iranian Math. Soc. 41:5 (2015), 1061-1070. · Zbl 1373.34035
[16] C.-F. Yang and A. Zettl, “Half inverse problems for quadratic pencils of Sturm-Liouville operators”, Taiwanese J. Math. 16:5 (2012), 1829-1846. · Zbl 1256.34013
[17] V.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.