Published online by Cambridge University Press: 24 October 2008
One of the most important techniques in the theory of non-linear differential equations is the direct method of Lyapunov and its extensions. It depends basically on the fact that a function satisfying the inequality
is majorized by the maximal solution of the equation
Using this comparison principle and the concept of Lyapunov's function various properties of solutions of differential equations have been considered (1–11).