ABSTRACT
This chapter deals with the analysis of systems of ordinary differential equations. It investigates nonautonomous systems of differential equations whose right-hand sides satisfy the conditions for existence of limiting differential equation systems. Through a combination of the comparison technique with the method of Lyapunov functions and the method of limiting equations, results are proved on the limiting behaviour of solutions, and asymptotic stability and instability, including stability with respect to some variables. The chapter shows how to prove some assertions about properties of the zero solutions of equations. It presents the theorems on stability and uniform asymptotic stability, and demonstrates that it is easy to prove some assertions on the stability of the solution x = 0 of the system.
