D. E. Limanska, G. E. Samkova

On the Existence of Analytic Solutions of Certain Types of Systems, Partially Resolved Relatively to the Derivatives in the Case of a Pole

For the systems of ordinary differential equations which are partially resolved relatively to the derivatives in the case of a pole, the theorems on the existence of at least one analytic in the complex domain solution of the Cauchy problem with an additional condition are established. Moreover, the asymptotic behavior of these solutions in this domain is studied.

Mathematics Subject Classification: 39A45

Key words and phrases: Ordinary differential equation, pole, Cauchy's problem, complex domain, singularity, asymptotic behavior, analytic solution