ON THE INVERSE PROBLEM FOR STURM-LIOUVILLE OPERATOR WITH A NONLINEAR SPECTRAL PARAMETER IN THE BOUNDARY CONDITION

Title & Authors
ON THE INVERSE PROBLEM FOR STURM-LIOUVILLE OPERATOR WITH A NONLINEAR SPECTRAL PARAMETER IN THE BOUNDARY CONDITION
Mamedov, Khanlar R.;

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, $\small{\infty}$). 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.
Keywords
inverse problem of scattering theory on half line;Sturm-Liouville operator with a nonlinear spectral parameter;scattering data;
Language
English
Cited by
1.
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2.
Inverse scattering problem for Sturm-Liouville operator with nonlinear dependence on the spectral parameter in the boundary condition, Mathematical Methods in the Applied Sciences, 2011, 34, 2, 231
3.
On an inverse scattering problem for a class of Dirac operators with spectral parameter in the boundary condition, Journal of Mathematical Analysis and Applications, 2012, 393, 2, 470
4.
On an Inverse Scattering Problem for a Discontinuous Sturm-Liouville Equation with a Spectral Parameter in the Boundary Condition, Boundary Value Problems, 2010, 2010, 1, 171967
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