Updated findings about the bounds and stability of solutions to a certain class of second-order vector differential equations

Abstract

Using an appropriate Lyapunov function, we prove in this study that for a certain system of second -order differential
equations, the zero-solution is stable when P(t, X, Y) = 0 and that all solutions are limited when P(t, X, Y) /= 0. The
findings presented in this publication add to and refine previous research. To back up the validity of the findings that
have been obtained, examples are provided.