Stability and Boundedness Properties of Certain Second-Order Differential Equations

Abstract

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 not equal 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. (c) 2006 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.