Some oscillation criteria for second order nonlinear functional ordinary differential equations

Abstract

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))'+δ 1 p(t)x'( t)+δ 2 q(t)f(x(g(t)))=0, for ≤ t 0≤t, where δ 1=± 1 and δ 2=± 1. The functions p,q,g:[t 0,∞)→ R, f:R → R are continuous, a(t)>0, p(t)≥ 0, q(t)≥ 0 for t≥ t 0, lim t→∞ g(t)=∞, and q is not identically zero on any subinterval of [ t 0,∞). Moreover, the functions q(t),g(t), and a(t) are continuously differentiable.