When a carbon nanotube emitter is operated at high currents (typically above 1 microA per emitter), a small voltage drop ( approximately few volts) along its length or at its contact generates a reverse/canceling electric field that causes a saturation-like deviation from the classical Fowler-Nordheim behavior with respect to the applied electric field. We present a correction to the Fowler-Nor...

Equation (2) has some oscillation behavior [1-3], In 2012, Liu [4] obtained some oscillation criteria of eq. (1). In the last decades, the Emden-Fowler equations have attracted extensive attention for the relevance to nuclear physics and gaseous dynamics in astrophysics, the oscillation behavior of the Emden-Fowler equations are studied by many scholars [5-10]. In this paper, we further study f...

We consider a quasilinear dynamic equation reducing to a half-linear equation, an Emden–Fowler equation or a Sturm–Liouville equation under some conditions. Any nontrivial solution of the quasilinear dynamic equation is eventually monotone. In other words, it can be either positive decreasing (negative increasing) or positive increasing (negative decreasing). In particular, we investigate the a...

All generators of the optimal algebra associated with a generalization Endem-Fowler equation are showed; some them allow to give invariant solutions. Variational symmetries and respective conservation laws also showed. Finally, representation Lie symmetry is showed by groups matrices.