In this paper we present the oscillation criterion for a class of fourth order nonlinear difference equations with quasidifferences.

The effect of surface tension on the Rayleigh-Taylor (RT) instability and Richtmyer – Meshkov (RM) instability induced development of nonlinear structures like spike and bubble at two fluid interface have been investigated .In case of RT instability, the surface tension reduces the velocity of the tip of both the bubble and the spike by the factor (1-k /3 kc ) where, kc =(h-l)g/T .For k > 3 k...

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

We develop higher-order nonlinear models of three-stage and five-stage ring oscillators based on a novel inverter model. The oscillation condition and oscillation frequency are derived and compared to classical linear model analysis. Two important special cases for five-stage ring oscillators are also studied. Numerical simulations are shown.

In this article we study the oscillation of solutions to the third order nonlinear functional dynamic equation

In this paper, we establish some new oscillation criteria for the third order nonlinear delay dynamic equations

In this article we establish an oscillation theorem for second order Sturm-Liouville difference equations with general nonlinear dependence on the spectral parameter l. This nonlinear dependence on l is allowed both in the leading coefficient and in the potential. We extend the traditional notions of eigenvalues and eigenfunctions to this more general setting. Our main result generalizes the re...

In this paper we establish some new oscillation criteria for the third-order nonlinear dynamic equation (c(t) ( (a(t)x(t)) )γ ) + f(t, x(t)) = 0, t ∈ [a,∞)T on time scales, where γ ≥ 1 is a quotient of odd integers. Our results not only unify the oscillation theory for third-order nonlinear differential and difference equations but also are new for the q-difference equations and can be applied ...

We study the dynamics of a laser-trapped nanoparticle in high vacuum. Using parametric coupling to an external excitation source, the linewidth of the nanoparticle's oscillation can be reduced by three orders of magnitude. We show that the oscillation of the nanoparticle and the excitation source are synchronized, exhibiting a well-defined phase relationship. Furthermore, the external source ca...

In this paper, we study the oscillation of nonlinear fractional nabla difference equations of the form [Formula: see text]where c and α are constants, [Formula: see text] is the Riemann-Liouville fractional nabla difference operator of order [Formula: see text] is a real number, and [Formula: see text]. Some sufficient conditions for oscillation are established.