Some oscillation criteria for second order nonlinear functional ordinary differential equations - Zayed, E.M.E.; El-Moneam, M.A. (Acta Mathematica Scientia, 2007)
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.