Volume no :53, Issue no: 1, September (2018)

Journal of Mathematical Sciences: Advances and Applications

THE ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF CERTAIN TYPES OF THE DIFFERENTIAL EQUATIONS PARTIALLY SOLVED RELATIVELY TO THE DERIVATIVES WITH A SINGULARITY IN THE ZERO-POINT

Author's: Diana Limanska and Galina Samkova
Pages: [21] - [40]
Received Date: July 9, 2018; Revised August 17, 2018
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100121985

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 behaviour of these solutions in this domain is studied.

Keywords

ordinary differential equation, pole, Cauchy’s problem, complex domain, singularity, asymptotic behaviour, analytic.