Oscillation Results for Third Order Nonlinear Delay Dynamic Equations on Time Scales

In this paper, we consider the third order nonlinear delay dynamic equations (a(t){[r(t)x(t)]}) + f(t, x(τ(t))) = 0, on a time scale T, where γ > 0 is a quotient of odd positive integers, a and r are positive rd-continuous functions on T, and the so-called delay function τ : T→ T satisfies τ(t) ≤ t, and τ(t)→∞ as t→∞, f ∈ C(T×R,R) is assumed to satisfy uf(t, u) > 0, for u 6= 0 and there exists a positive rd-continuous function p on T such that f(t, u)/uγ ≥ p(t), for u 6= 0. We establish some new results. Some examples are considered to illustrate the main results. 2010 Mathematics Subject Classification: 39A21, 34C10, 34K11, 34N05