The structure of Gelfand-Levitan-Marchenko type equations for Delsarte   transmutation operators of linear multi-dimensional differential operators   and operator pencils. Part 1
  An analog of Gelfand-Levitan-Marchenko integral equations for multi- dimensional Delsarte transmutation operators is constructed by means of studying their differential-geometric structure based on the classical Lagrange identity for a formally conjugated pair of differential operators. An extension of the method for the case of affine pencils of differential operators is suggested. 
J. Golenia, A.K. Prykarpatsky, Y.A. Prykarpatsky