Some oscillation criteria for second order nonlinear functional ordinary differential equations

The main objective of this article is to study the oscillatory behavior of the solutions of the following nonlinear functional differential equations

(a(t)x'(t))'+δ₁p(t)x'(t)+δ₂q(t)f(x(g(t)))=0,

for ≤ t₀≤t, where δ₁=± 1 and δ₂=± 1. The functions p,q,g:t₀,∞)→ R, f:R → R are continuous, a(t)>0, p(t)≥ 0,q(t)≥ 0 for t≥ t₀, lim_t→∞g(t)=∞, and q is not identically zero on any subinterval of t₀,∞). Moreover, the functions q(t),g(t), and a(t) are continuously differentiable.