In this note, we examine the oscillatory nature for the fourth-order nonlinear delay dynamic equation (r(t)x 3 (t)) + p(t)x(τ(t)) = 0 on a time scale T unbounded above. Some oscillation criteria are obtained for the cases when ∫ ∞

This work is concerned with oscillation of a class of fourth-order nonlinear delay dynamic equations on a time scale. A new comparison theorem is established that improves related results reported in the literature.

We present new oscillation criteria for the second order nonlinear damped delay dynamic equation (r(t)(x(t))) + p(t)(x(t)) + q(t)f (x(τ(t))) = 0. Our results generalize and improve some known results for oscillation of second order nonlinear delay dynamic equation. Our results are illustrated with examples.

The theory of time scales was introduced by Hilger in his Ph.D. thesis 1 in 1988 in order to unify continuous and discrete analysis. The study of dynamic equations on time scales is a fairly new subject and research in this area is rapidly growing. For some basic definitions and relevant results on time scales, see 2, 3 . Recently, first-order boundary value problems BVPs for short on time scal...

In this paper, we establish several oscillation criteria for the nonlinear second-order damped delay dynamic equation ( r(t)|xΔ(t)|β−1xΔ(t) )Δ + p(t)|xΔσ(t)|β−1xΔσ(t) + q(t)f(x(τ(t))) = 0 on an arbitrary time scale T, where β > 0 is a constant. Our results generalize and improve some known results in which β > 0 is a quotient of odd positive integers. Some examples are given to illustrate our m...

In this paper, by constructing a class of Philos type functions on time scales, we investigate the oscillation of the following second-order forced nonlinear dynamic equation x(t)− p(t)|x(q(t))|x(q(t)) = e(t), t ∈ T where T is a time scale, p, e : T → R are right dense continuous functions with p > 0, λ > 1 is a constant, and q(t) = t or q(t) = σ(t). Our results not only unify the oscillation o...

By means of Riccati transformation techniques, we establish some new oscillation criteria for the second order nonlinear dynamic equation