The author considers the nonlinear third order ordinary differential equation
or its equivalent system
where it is assumed that , , and are continuous functions which depend only on the arguments displayed explicitly, the dots denote differentiation with respect to and the derivatives and exist and are continuous.
Some sufficient conditions have been established for the ultimate boundedness of all solutions of (1). By this way, the author’s result improves the result obtained by the reviewer [C. Tunç, JIPAM, J. Inequal. Pure Appl. Math. 6, No. 1, Paper No. 3, 6 p., electronic only (2005; Zbl 1082.34514)].