Power expansions of solutions of a system of algebraic and differential equations. (Q1432646)

The author suggests generalizations of the classical Cauchy and Cauchy-Kovalevskaya theorems on the existence and uniqueness of an analytical solution to a system of analytical or differential equations. These generalizations are given in terms of power geometry [the author, Power geometry in algebraic and differential equations. North-Holland Mathematical Library 57. Amsterdam: North-Holland (2000; Zbl 0955.34002)]. This paper is a continuation of [Dokl. Math. 64, No. 2, 160--164 (2001; Zbl 1052.34009)].