Oscillation of third-order neutral differential equations

The objective of this paper is to study asymptotic properties of the couple of third-order neutral differential equations ( E ± ) [ a ( t ) ( [ x ( t ) ± p ( t ) x ( δ ( t ) ) ] ″ ) γ ] ′ + q ( t ) x γ ( τ ( t ) ) = 0 , t ≥ t 0 , where a ( t ) , q ( t ) , p ( t )  are positive functions, γ > 0  is a quotient of odd positive integers and τ ( t ) ≤ t , δ ( t ) ≤ t . We will establish some sufficient conditions which ensure that all nonoscillatory solutions of ( E ± ) converge to zero. Some examples are considered to illustrate the main results.