Asymptotic solutions of forced nonlinear second order differential equations and their extensions

Using a modified version of Schauder's fixed point theorem, measures of non-compactness and classical techniques, we provide new general results on the asymptotic behavior and the non-oscillation of second order scalar nonlinear differential equations on a half-axis. In addition, we extend the methods and present new similar results for integral equations and Volterra-Stieltjes integral equations, a framework whose benefits include the unification of second order difference and differential equations. In so doing, we enlarge the class of nonlinearities and in some cases remove the distinction between superlinear, sublinear, and linear differential equations that is normally found in the literature. An update of papers, past and present, in the theory of Volterra-Stieltjes integral equations is also presented

On the behaviour of solutions of neutral impulsive difference equations of second order

The work embodied in this paper is the study of oscillation properties of a class of second order neutral impulsive difference equations with constant coefficients. In addition, an effort is made here to apply constant coefficient results to nonlinear impulsive difference equations with variable coefficients

Oscillation results for second-order nonlinear neutral differential equations

Published version of an article in the journal: Advances in Difference Equations. Also available from the publisher at: http://dx.doi.org/10.1186/1687-1847-2013-336 Open AccessWe obtain several oscillation criteria for a class of second-order nonlinear neutral differential equations. New theorems extend a number of related results reported in the literature and can be used in cases where known theorems fail to apply. Two illustrative examples are provided

How BAO measurements can fail to detect quintessence

We model the nonlinear growth of cosmic structure in different dark energy models, using large volume N-body simulations. We consider a range of quintessence models which feature both rapidly and slowly varying dark energy equations of state, and compare the growth of structure to that in a universe with a cosmological constant. The adoption of a quintessence model changes the expansion history of the universe, the form of the linear theory power spectrum and can alter key observables, such as the horizon scale and the distance to last scattering. The difference in structure formation can be explained to first order by the difference in growth factor at a given epoch; this scaling also accounts for the nonlinear growth at the 15% level. We find that quintessence models which feature late $(z<2)$, rapid transitions towards $w=-1$ in the equation of state, can have identical baryonic acoustic oscillation (BAO) peak positions to those in $\Lambda$CDM, despite being very different from $\Lambda$CDM both today and at high redshifts $(z \sim 1000)$. We find that a second class of models which feature non-negligible amounts of dark energy at early times cannot be distinguished from $\Lambda$CDM using measurements of the mass function or the BAO. These results highlight the need to accurately model quintessence dark energy in N-body simulations when testing cosmological probes of dynamical dark energy.Comment: 10 pages, 7 figures, to appear in the Invisible Univers International Conference AIP proceedings serie

Oscillatory Properties of Solutions of the Fourth Order Difference Equations with Quasidifferences

A class of fourth--order neutral type difference equations with quasidifferences and deviating arguments is considered. Our approach is based on studying the considered equation as a system of a four--dimensional difference system. The sufficient conditions under which the considered equation has no quickly oscillatory solutions are given

Systematic Derivation for Quadrature Oscillators Using CCCCTAs

According to 16 nullor-mirror models of the current-controlled current conveyor transconductance amplifier (CCCCTA) and using nodal admittance matrix (NAM) expansion method, three different classes of the double-mode quadrature oscillators employed CCCCTAs and two grounded capacitors are synthesized. The class I oscillators have 32 different forms, the class II oscillators have 16 different forms, and the class III oscillators have four different forms. In all, 52 quadrature oscillators using CCCCTAs are obtained. Having used canonic number of components, the circuits are easy to be integrated and the condition for oscillation and the frequency of oscillation can be tuned by tuning bias currents of the CCCCTAs. The circuit analysis and simulation results have been included to support the generation method