ABSTRACT
Definition of Lyapunov Function We turn now to an entirely different method for studying the stability properties of a given solution. This method, the Lyapunov second method or direct method, uses an approach different from that used in the preceding chapter. It requires no study of the linear parts of equations (eigenvalues or characteristic exponents) and no knowledge is needed of solutions near the solution under study. Of course another price has to be paid: application of Lyapunov’s second method demands the construction of the Lyapunov functions to be described later. Such constructions are generally difficult and have been made only for certain classes of equations.
