About Uniform Boundedness and Convergence of Solutions of Certain Non-Linear Differential Equations of Fifth-Order

Abstract

In this paper, we establish sufficient conditions under which all solutions of equation of the type X-(5) + f (t, (x)over dot, (x)double over dot, (x) triple over dot, x((4))) + phi(t, (x)over dot, <(x)double over dot>, (x) triple over dot) + phi (t, x, (x)over dot, <(x)double over dot>) + g(t, x, (x)over dot) + e(t)h(x) = p(t, x, (x)over dot, <(x)double over dot>, (x) triple over dot, x((4))) are uniformly bounded and tend to zero as t -> infinity. Our theorem is stated in a more general form; it extends some related results known in the literature. Also, the relevance of our result is to show that the results established in Abou El-Ela and Sadek [2,3] and Sadek [13] contain some superfluous conditions.