THE ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF THE SYSTEM OF THE DIFFERENTIAL EQUATIONS PARTIALLY SOLVED RELATIVELY TO THE DERIVATIVES WITH NON-SQUARE MATRICES

THE ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF THE SYSTEM OF THE DIFFERENTIAL EQUATIONS PARTIALLY SOLVED RELATIVELY TO THE DERIVATIVES WITH NON-SQUARE MATRICES

D. Limanska

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Abstract

The systems of ordinary dierential equations, which are partially resolved relatively to the derivatives, were considered in case of a removable singularity and in case of a pole. The theorems on the existence of at least one analytic solution in the complex domain of the Cauchy problem with an additional condition are established for both cases. Moreover, the asymptotic behavior of these solutions in this domain is studied.

Keywords

Ordinary dierential equation, pole, Cauchy's problem; complex domain, singularity, asymptotic behavior.