Stability and Boundedness Results for Certain Nonlinear Vector Differential Equations of the Fourth Order

Abstract

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. © 2006 Springer Science+Business Media, Inc.