A method of normal forms for nonlinear singularly perturbed systems in case of intersection of eigenvalues of limit operator

The Lomov regularization method is generalized on weakly nonlinear singularly perturbed problems in the case of intersection of the roots of the characteristic equation of the limit operator. To construct asymptotic solutions, we use the idea of initial problems with the use of normal forms, first realized in nonlinear systems by Safonov V.F. and Bobodzhanov A.A.