Asymptotic Behavior and Oscillations of Second Order Differential Equations with Deviating Argument

The asymptotic behavior of the solutions of the second order differential equation with deviating argument ax9.9qbx9qcxsfwt, x t., x9 t., x f t.., x9 f t..x is studied. Our technique depends on an integral inequality containing a deviating argument. For special classes of these equations the explicit asymptotic behavior is obtained. From this asymptotic behavior the oscillation of the solutions is evident. Q 1996 Academic Press, Inc.