On an Abstract Nonlinear Cauchy-Kowalewski Theorem – a Variant of L. Nirenberg’s and T. Nishida’s Proof

Abstract

The paper deals with a variant of the proof of an abstract nonlinear Cauchy-Kowalewski theorem. The original proof as well as its modification regarded in this paper make use of the method of successive approximations where in both cases the interval of convergence is characterized by an infinite product. In the present paper the infinite product of the original proof is replaced by one with arbitrary factors. In this way in some cases the convergence is proved in a larger interval.