Journal of Applied Mathematics and Stochastic Analysis
Volume 6 (1993), Issue 1, Pages 69-81

Constructive method for solving a nonlinear singularly perturbed system of differential equations in critical case

Angela Slavova

Florida Institute of Technology, 150 W. University Blvd., Melbourne 32901-6988, Florida, USA

Received 1 November 1992; Revised 1 March 1993

Copyright © 1993 Angela Slavova. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A singularly, perturbed system of differential equations with degenerate matrix at the derivative is considered. The existence and construction of the periodic solutions are investigated in critical case. For the analysis of these algorithms the apparatus of Lyapunov's finite majorizing equations is used. An implementation of this method is given in two examples.