Stability and boundedness results for certain nonlinear vector differential equations of the fourth order

We consider the equation X ⁽⁴⁾ + Φ(X″)X‴ + F(X,X′)X″ + G(X′) + H(X) = P(t,X,X′,X″,X‴) in two cases: P ≡ 0 and P ≠ 0. In the case P ≡ 0, the asymptotic stability of the zero solution X = 0 of the equation is investigated; in the case P ≠ 0, the boundedness of all solutions of the equation is proved. Published in Neliniini Kolyvannya, Vol. 9, No. 4, pp. 548–563, October–December, 2006.