关键词: Oscillatory and nonoscillatory solutions, nonlinear functional 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))'+δ₁p(t)x'(t)+δ₂q(t)f(x(g(t)))=0,
for 0≤ 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.

Key words: Oscillatory and nonoscillatory solutions, nonlinear functional differential equations