Oscillation Theorems for Third-Order Half-linear Delay Dynamic Equations with Damping

This article is concerned with oscillatory behavior of a class of third order half-linear delay dynamic equation with damping ( r(x 2 ) ) (t)+ p(t) ( x 2 )γ (t)+ q(t)x (τ (t)) = 0, on an arbitrary time scaleTwith supT = ∞ and lim t→∞ τ(t) = ∞.We establish some new sufficient conditions which ensure that every solution oscillates or converges to zero. Example is given to illustrate our main results. AMS subject classification: 34K11, 39A10, 34N05.