A note on the continuability and boundedness of solutions to a class of vector differential equations of third order with finite delay

In this article, we use Lyapunov's second (or direct) method, by building an appropriate Lyapunov functional. Sufficient conditions which warrant the continuability and boundedness of all solutions to a kind of nonlinear vector differential equations of third order with constant retarded argument are established. Also, we give an example to describe the theoretical analysis in this study and to check the impressiveness of the method employed.Mathematics Subject Classication (2010): 34C11, 34K20, 45J05.Key words: Integro-differential equation, delay, continuability, boundedness