Solvability of a class of integro-differential equations and connections to one-dimensional inverse problems |
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Authors: | Yilian Zhang |
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Institution: | Department of Mathematical Science, University of South Carolina Aiken, Aiken, SC 29801, USA |
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Abstract: | A new approach to one-dimensional inverse problem was recently introduced by Barry Simon. We continue the study on an intermediate object A, which satisfies a nonlinear integro-differential equation. We prove local solvability of this A-equation and find a necessary condition for global solvability. Some exact solutions are presented. |
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Keywords: | Inverse problem Integro-differential equation A-equation |
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