NEW RESULTS ON THE CONVERGENCE OF SOLUTIONS FOR A CERTAIN FOURTH ORDER NONLINEAR DIFFERENTIAL EQUATION

This paper is concerned with the convergence of solutions to the fourth order nonlinear differential equation x(iv) + phi((x) triple over dot + f((x)double over dot) + f((x)over dot) + h(x) = p(t, (x)over dot, (x)double over dot, (x) triple over dot) where the nonlinear functions phi, f, g, h and p are continuous. By constructing a complete Lyapunov function, kune fundamental questions on whether convergence results on the above equation which do not appear to have received any attention in the literature can be proved, are answered.