Constructive Approach for Solving Nonlinear Singularly Perturbed Systems with Nonconstant Matrix at the Derivative

In this paper we study singularly perturbed systems of differential and integro-differential equations with variable coefficients in the case when a matrix at the derivative is singular. Existence and construction of the solutions are investigated using iterative processes convergent in Cauchy′s sense. For the analysis of these algorithms Lyapunov′s majorizing equations method is applied.