Stability and boundedness properties of certain second-order differential equations

摘要

In this paper, we investigated the differential equation X + 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.