Continuity of the scattering function and Levinson‐type formula of Klein–Gordon equation |
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| Authors: | Özkan Karaman Nida P Kosar |
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| Institution: | 1. Department of Mathematics, Faculty of Sciences and Letters, K.?Maras Sutcu Imam University, , Avsar Campus, 46100 Kahramanmaras, Turkey;2. Department of Mathematics, Faculty of Sciences and Letters, Bitlis Eren University, , Bitlis, Turkey |
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| Abstract: | We considered the inverse problem of scattering theory for a boundary value problem on the half line generated by Klein–Gordon differential equation with a nonlinear spectral parameter‐dependent boundary condition. We defined the scattering data, and we proved the continuity of the scattering function S(λ); in a special case, the relation for the difference of the logarithm of the scattering function, which is called the Levinson‐type formula, was obtained. Copyright © 2012 John Wiley & Sons, Ltd. |
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| Keywords: | inverse problem on half line Gelfand– Levitan– Marchenko equation scattering function scattering data Levinson‐type formula |
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