SOLUTIONS OF ANALYTICAL SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS

Abstract. In this paper are examined some classes of linear and non-linear analytical systems of partial differential equations. Compatibility conditions are found and if they are satisfied, the solutions are given as functional series in a neighborhood of a given point (x = 0). 1. Introduction. This paper is a continuation of the papers [2] – [5], and we will give a brief view of them. In the paper [2] it was found a formula for the k-th covariant derivative. Further that formula was generalized for k ∈ R. Especially, if k = −1 it yields to a general solution for a system of linear differential equations [3]. In the paper [4] is given a