BOUNDEDNESS CRITERIA FOR A CLASS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH DELAY

We consider certain class of second order nonlinear nonautonomous delay differential equations of the form a(t)x '' + b(t)g (x, x') + c(t)h(x(t - r))m(x') = p(t, x, x') and (a(t)x')' + b(t)g(x, x') + c(t)h(x(t - r))m(x') = p(t, x, x'), where a, b, c, g, h, m and p are real valued functions which depend at most on the arguments displayed explicitly and r is a positive constant. Different forms of the integral inequality method were used to investigate the boundedness of all solutions and their derivatives. Here, we do not require construction of the Lyapunov-Krasovski.i functional to establish our results. This work extends and improve on some results in the literature.