OSCILLATION CRITERIA OF COMPARISON TYPE FOR NONLINEAR FUNCTIONAL-DIFFERENTIAL EQUATIONS

In this paper we relate the oscillation problem of the nonlinear funct ional differential equation a(t) x'(t))' + q(t) f(x(g(t))) = 0 and the nonlinear neutral functional differential equation (a(t)(x(t) + p(t) x(g(t)))')' + q(t) f(x(g(t))) = 0 to some linear second order ordinar y differential equations. Recent results on linear oscillation can thu s be used to obtain interesting oscillation criteria for the nonlinear equations. Similar results for the forced nonlinear functional differ ential equation (a(t) x'(t))' + q(t) f(x(g(t)))= e(t) and the forced n eutral functional differential equation (a(t) (x(t) + mx(t - n))')' q(t) f(x(g(t)))= e(t) are also established. The function f appeared in the above equations is not required to be monotone.