ABSTRACT
In this section we discuss the applicability of the Newton-Kantorovich method to the nonlinear partial integral equation of Uryson type
by means of the Newton-Kantorovich method. A basic ingredient of this method consists in verifying a local Lipschitz condition for the Frechet derivative of the the corresponding nonlinear partial integral operators. The abstract results are illustrated in the spaces C and L, for 1 S p S 00. In particular, we show that a local Lipschitz condition for the derivative in L, for p < 00 leads to a strong degeneracy of the corresponding kernels. The basic results of this section are taken from ApPELL-DE PASCALE-KALITVIN-ZABREJKO [1996].
