Abstract :
In this paper, we study the problems of the ultimate boundedness and periodicity of solutions of the third order system of nonlinear differential equations, X⃛ + AẌ + BẊ + H(X) = P(t, X, Ẋ, Ẍ, X⃛), (*) where A, B are real n × n constant symmetric matrices and X ∈ Rn. We obtain some sufficient conditions which ensure that all the solutions of Eq. (*) are ultimately bounded, and we also give some sufficient conditions which guarantee that there exists at least one periodic solution of Eq. (*). Our results revise and improve those results obtained by Afuwape (J. Math. Anal. Appl.97 (1983), 140-150) (which are not applicable to all equations of the general form (*)).
