On the holomorphic regularization of singularly perturbed systems of differential equations

Resumo

A method for constructing pseudo-holomorphic solutions to strongly nonlinear singularly perturbed systems of differential equations, which a logical continuation of the Lomov regularization method, is proposed. The existence of integrals of such systems, holomorphic in the small parameter, is proven, and sufficient conditions for the convergence of expansion of solutions to these systems in powers of the small parameter in the usual sense are obtained.