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 equation(E)[a(t)[x″(t)]γ]′+q(t)f(x[τ(t)])=0.[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.