**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

**abstract:**

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