Oscillation Criteria for Certain Forced Second-Order Nonlinear Differential Equations with Delayed Argument

摘要

Some new sufficient conditions for the oscillation criteria are given for the forced second-order nonlinear differential equations with delayed argument in the form, x″(t) + q(t) f (x(τ(t))) = e(t). The results are based on the information only on a sequence of subintervals of [t_0, ∞) rather than on the whole half-line. Our methodology is somewhat different from that of previous authors. Our results generalize and extend some earlier results of Sun. Furthermore, we are able to answer the question in recent paper for the oscillation of bounded solutions of the above equation when f(x) = | x |~λsgn x, 0 < λ < 1.