Oscillation of third-order nonlinear differential equations

The objective of this work is to study oscillatory and asymptotic properties of the third-order nonlinear delay differential equation (E) [ a ( t ) [ x ″ ( t ) ] γ ] ′ + q ( t ) f ( x [ τ ( t ) ] ) = 0 . Applying suitable comparison theorems we present new criteria for oscillation or certain asymptotic behaviors of nonoscillatory solutions of Eq. (E). The results obtained essentially improve and complement earlier ones.