On the Behavior of Solutions of Some Systems of Differential Equations Partially Solved with Respect to the Derivatives in the Presence of a Pole

Abstract

We study the existence of analytic solutions for some systems of ordinary differential equations partially solvable with respect to the derivatives. We establish sufficient conditions for the existence of analytic solutions of the Cauchy problem in the presence of a pole. An estimate for these solutions is obtained in a certain domain and the problem of the number of solutions is investigated.