In this article, we study the oscillation of second-order nonlinear impulsive dynamic equations on time scales. Using Riccati transformation techniques, we obtain sufficient conditions for oscillation of all solutions. An example is given to show that the impulses play a dominant part in oscillations of dynamic equations on time scales.

By means of Riccati transformation techniques, we establish some oscillation criteria for a second order nonlinear dynamic equation on time scales in terms of the coefficients. We give examples of dynamic equations to which previously known oscillation criteria are not applicable.

In this paper, we discuss the oscillation of certain second-order nonlinear dynamic equations on time scales. We establish some oscillation criteria for the equations by applying a generalized Riccati transformation technique. Our results improve and extend some known results in the recent literature. Mathematics Subject Classification: 39A10

We show experimentally that parametric interaction can induce a cooperative oscillation of non-simultaneously resonant transverse modes in an optical parametric oscillator. More generally, this effect is expected to occur in any spatially extended system subjected to boundary conditions where nonlinear wave mixing of two nonresonant spatial modes can generate a resonant oscillation.

We present new interval oscillation criteria for certain nonlinear delay second order differential equation that are different from some known ones. Our results extend and improve some previous oscillation criteria and handle the cases which are not covered by known results. In particular, several examples that dwell upon the sharp condition of our results are also included.

The main objective of this paper is to study the qualitative behavior for a class of nonlinear rational difference equation. We study the local stability, periodicity, Oscillation, boundedness, and the global stability for the positive solutions of equation. Examples illustrate the importance of the results Keywords— Difference equation, stability, oscillation, boundedness, globale stability an...

This paper summarizes a series of results on the oscillation of impulsive ordinary differential equations. We consider linear, half-linear, super-half-linear, and nonlinear equations. Several oscillation criteria are given. The Sturmian comparison theory for linear and half linear equations is also included.

This paper is concerned with the oscillation of second-order nonlinear neutral differential equations of the form [ r(t)[(x(t) + p(t)x(σ(t)))′]γ ]′ + f(t, x(τ(t))) = 0, by using a generalized Riccati’s technique and integral averaging technique, we establish new oscillation results which handle some cases not covered by known criteria.

Much of the existing literature on dielectric elastomers has focused on quasi-static deformation. However, in some potential applications, the elastomer deforms at high frequencies and undergoes nonlinear oscillation. While nonlinear oscillation has been studied in many areas of science and engineering, we are unaware of any theoretical analysis of nonlinear oscillation of dielectric elastomers...

A smooth transition autoregressive model is estimated for the Southern Oscillation Index, an index commonly used as a measure of El Niño events. Using standard measures there is no indication of nonstationarity in the index. A logistic smooth transition autoregressive model describes the most turbulent periods in the data (these correspond to El Niño events) better than a linear autoregressive ...