Comments on "An energy metric algorithm for the generation of Liapunov functions"

On the stability and boundedness of solutions to third order nonlinear differential equations with retarded argument

“…Meanwhile, it should be noted that, in 1969, Palusinski et al [13] applied an energy metric algorithm for the generation of the Lyapunov function for third order ordinary nonlinear differential equation without delay:…”

“…The motivation for the present work has been inspired basically by the paper of Palusinski et al [13] and the papers listed above. Our aim is to extend and improve the result established by Palusinski et al [13] to nonlinear delay differential equation (1) for the asymptotic stability of trivial solution and boundedness of all solutions, when p ≡ 0 and p = 0 in (1), respectively. We also give two examples on the stability and boundedness of solutions to some specific delay differential equations of third order.…”

On the stability and boundedness of a class of higher order delay differential equations

“…At the same time, for some papers published on the qualitative behaviors of solutions of various nonlinear third order differential equations with delay or without delay, we refer the reader to the papers of Palusinski et al [3], and the references thereof.…”