Boundedness and Stability Properties of Solutions of Certain Fourth Order Differential Equations Via the Intrinsic Method

Abstract

In this paper, firstly a Lyapunov function is derived for (1.2) by applying the intrinsic method introduced by Chin[6], Secondly equation (1.2) is examined in two cases: (i) P s 0, (ii) P ∗ 0. For case (i) the asymptotic stability in the large of the trivial solution x = 0 is investigated and for case (ii) the boundedness results are obtained for solutions of equation (1.2). These results improve and include several well-known results. © 1996, Oldenbourg Wissenschaftsverlag GmbH, Rosenheimer Str. 145, 81671 München. All rights reserved.