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In this paper, by using the Riccati technique which reduces the higher order dynamic equations to a Riccati dynamic inequality, we will establish some new sufficient conditions for oscillation of the second order nonlinear neutral dynamic equation (r(t)((x(t) + p(t)x(τ(t)))Δ)γ)Δ + q(t)xα(δ(t)) + v(t)xβ(η(t)) = 0; on time scales where γ, α, β, are quotient of odd positive integers. [ABSTRACT FROM AUTHOR]

In this paper, we will establish some new sufficient condition for oscillation of solutions of a certain class of first-order neutral delay difference equations of the form Δ (xn -- pnxn-1) + qnxn-τγ = 0, where γ is a quotient of odd positive integers. We will consider the sublinear and super linear cases. The results will be obtained by using the oscillation theorems of second order delay difference equations. [ABSTRACT FROM AUTHOR]

In this paper, we prove some new characterizations of weights in some Hardy-type inequalities on time scales. The results as special cases contain the results due to Beesack and Heinig, Leindler and Bloom and Kerman. Some new integral and discrete inequalities related to Copson's, Flett's, Bliss's and Bennett's will be formulated. The main results will be proved by using new generalizations of Opial's type inequalities, Hölder's inequality, Minkowski's inequality and the chain rule on time scales. [ABSTRACT FROM AUTHOR]

In this paper, we extend and improve some dynamic inequalities by using the sneak-out principle with di¤erent exponents on time scales. The main results can be used to formulate the corresponding discrete inequalities of Bennett and G-Erdmann type. [ABSTRACT FROM AUTHOR]