Solvability of a class of integro-differential equations and connections to one-dimensional inverse problems

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. © 2005 Elsevier Inc. All rights reserved.