Oscillatory behavior of higher order nonlinear neutral forced differential equations with oscillating coefficients

In this paper, the higher order nonlinear neutral forced differential equations of the form [x(t)−p(t)x(τ(t))](n)+∑i=1mqi(t)fi(x(σi(t)))=s(t),t≥t0, where n,m∈Nn,m∈N, n≥2n≥2 and m≥1m≥1, are studied. A new necessary and sufficient theorem for the oscillation of bounded solutions and a sufficient criterion for the existence of bounded positive solutions of the above equations are obtained for general p(t)p(t) and s(t)s(t). In particular, our results improve some known results.