Stability and boundedness properties of certain second-order differential equations

In this paper, we investigated the differential equationX¨+A(t)F(X)=P(t,X,X˙)in two cases; (a) P≡0 and (b) P≠0. For the case (a), the stability of the solution X=0 and the uniform boundedness of all solutions of this equation are investigated; in the case (b) the boundedness of all solutions of the same equation is discussed.