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On the inverse problem for Sturm-Liouville operator with a nonlinear spectral parameter in the boundary condition

Khanlar R. Mamedov
대한수학회 (The Korean Mathematical Society)|2009.11|대한수학회지 (Journal of the KMS)|제46권 제6호|pp. 1243-1254

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참고문헌

키워드

inverse problem of scattering theory on half linescattering data
주제분류수학

초록

The inverse scattering problem is investigated for some second order differential equation with a nonlinear spectral parameter in the boundary condition on the half line [0,∞). In the present paper the coefficient of spectral parameter is not a pure imaginary number and the boundary value problem is not selfadjoint. We define the scattering data of the problem, derive the main integral equation and show that the potential is uniquely recovered.

Abstract

The inverse scattering problem is investigated for some second order differential equation with a nonlinear spectral parameter in the boundary condition on the half line [0,∞). In the present paper the coefficient of spectral parameter is not a pure imaginary number and the boundary value problem is not selfadjoint. We define the scattering data of the problem, derive the main integral equation and show that the potential is uniquely recovered.

참고문헌 (15)

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  8. Kh. R. Mamedov, "On the inverse problem of scattering theory for a differential operator of the second order, Functional analysis and its applications", North-Holland Math. Stud., 197, pp.185~194 (2004), Elsevier
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관련 논문AI추천

ON A DIRECT PROBLEM OF SCATTERING THEORY FOR A CLASS OF STURM-LIOUVILLE OPERATOR WITH DISCONTINOUS COEFFICIENTMamedov, Palamut장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2009 · 제12권 제2호On a spectral expansion formula for a class of second order differential equation with discontinuous coefficientF. A. Cetinkaya, Kh. R. Mamedov장전수학회 · Advanced Studies in Contemporary Mathematics2014 · 제24권 제4호Uniqueness of the solution of half inverse problem for the impulsive Sturm Liouville operatorA. Sinan Ozkan, Baki Keskin, Yasar Cakmak대한수학회 · 대한수학회보2013 · 제50권 제2호THE REGULARIZED TRACE FORMULA FOR A DIFFERENTIAL OPERATOR WITH UNBOUNDED OPERATOR COEFFICIENTA. Bayramov, E. Şen, K. Oruçoğlu장전수학회 · Advanced Studies in Contemporary Mathematics2015 · 제25권 제4호Spectral Analysis of Four Term Differential OperatorNyamwala Fredrick Oluoch경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2010 · 제50권 제1호ON THE UNIFORM CONVERGENCE OF SPECTRAL EXPANSIONS FOR A SPECTRAL PROBLEM WITH A BOUNDARY CONDITION RATIONALLY DEPENDING ON THE EIGENPARAMETEREmir A. Maris, Nazim B. Kerimov, Sertac Goktas대한수학회 · 대한수학회지2017 · 제54권 제4호

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