Forced oscillation of second order differential equations with mixed nonlinearities

This article is concerned with the oscillation of the forced second order differential equation with mixed nonlinearities (a(t)(x′(t))γ)′+po(t)xγ(go(t))+∑i=1npi(t)|x(gi(t))|αisgnx(gi(t))=e(t) where γ is a quotient of odd positive integers, αi > 0, i = 1, 2, …, n, a, e  , and pi∈C([0,∞),ℝ),a(t)>o,gi:ℝ→ℝpi∈C([0,∞),ℝ),a(t)>o,gi:ℝ→ℝ are positive continuous functions on ℝ with limt→∞gi(t)=∞,i=0,1,…,n Our results generalize and improve the results in a recent article by Sun and Wong [29].