Studies of solutions of singularly perturbed ordinary differential equations

The eigenvalues of the Jordan matrix determine different types of stability. It is not always possible to obtain asymptotic estimates in the real axis. Therefore, in this paper we will consider the types of stability that can be estimated in the real axis. The problem under consideration is nonlinear, so it is possible to obtain an estimate for the delay of the loss of stability in the real domain. To calculate the integral, we apply the second theorem on the average in a certain integral. We prove the theorem as a result, we obtain an estimate of singularly perturbed ordinary differential equations.