On the construction of stability regions for solutions of differential equations depending on parameters

The paper proposes a new general approach that allows one to study the problem of constructing stability regions for nonlinear differential equations. The approach is based on the modification of M. Rozo's method for studying stability of linear systems with periodic coefficients depending on a small parameter and also on asymptotic formulae of the perturbation theory for linear operators. Approximate formulae describing boundaries of stability regions are obtained.