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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 establish some interval oscillation criteria for impulsive conformable fractional partial delay differential equations with a forced term. The main results will be obtained by employing Riccati technique. Our results extend and improve some results reported in the literature for the classical differential equations without impulses. An example is provided to illustrate the relevance of the new theorems. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with oscillation of the nonlinear difference equation Δ(cn[Δ(dnΔxn)]γ) +qnf(xg(n))=0, n≥n0, where γ > 0 is the quotient of odd positive integers, cn, dn and qn are positive sequences of real numbers, g(n) is a sequence of nonnegative integers and f ϵ C(R,R) such that u f (u) > 0 for u ≠ 0. We establish some new sufficient conditions for oscillation by employing the Riccati substitution and the analysis of the associated Riccati difference inequality. Our results extend and improve some previously obtained ones. Some examples are considered to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, we will establish some new interval oscillation criteria for the forced second-order nonlinear dynamic equation[image omitted] on a time scale  where γ ≥ 1. As a special case when  =  our results not only include the oscillation results for second-order differential equations established by Wong (Oscillation criteria for a forced second-order linear differential equation, J. Math. Anal. Appl. 231 (1999), pp. 233-240) and Nasr (Sufficient condition for the oscillation of forced super-linear second order differential equations with oscillatory potential, Proc. Amer. math. Soc. 126 (1998), pp. 123-125) but also improve these results. When  = ,  = h or  = qN, i.e. for difference equations, generalized difference equations or q-difference equations our results are essentially new and also can be applied on different types of time scales, as illustrated in several examples. [ABSTRACT FROM AUTHOR]

In this paper, we consider the discrete non-linear delay population dynamics model [ABSTRACT FROM PUBLISHER]

In this paper, we discuss the oscillatory behavior of the second-order forced nonlinear dynamic equation (a(t)xΔ(t))+p(t)f(xο)=r(t), on a time scale T when a(t) > 0. We establish some sufficient conditions which ensure that every solution oscillates or satisfies lim inft→∞ |x(t)| = 0. Our oscillation results when r(t) = 0 improve the oscillation results for dynamic equations on time scales that has been established by Erbe and Peterson [Proc. Amer. Math. Soc 132 (2004), 735-744], Bohner, Erbe and Peterson [J. Math. Anal. Appl. 301 (2005), 491-507] since our results do not require ∫∞t0 q(t)Δt > 0 and ∫±∞± t0 du/f(u) < ∞. Also, as a special case when T = R, and r(t) = 0 our results improve some oscillation results for differential equations. Some examples are given to illustrate the main results. [ABSTRACT FROM AUTHOR]

This paper studies the nonlinear delay impulsive respiratory dynamics model. The model describes the sudden changes of the concentration of CO2 in the blood of the mammal. It is proved that the model has a unique positive periodic solution. Some sufficient conditions for oscillation of all positive solutions about the positive periodic solution are established and also some sufficient conditions for the global attractivity of the periodic solution are obtained. [ABSTRACT FROM AUTHOR]

New oscillation criteria for the second order nonlinear neutral delay differential equation [y(t)=p(t)y(t-ϒ)]-+q(t) f(y(g(t))) = 0, t ≥ t0 are given. The relevance of our theorems becomes clear due to a carefully selected example. [ABSTRACT FROM AUTHOR]