We establish some new oscillation criteria for the second-order quasilinear neutral delay dynamic equations r t zΔ t γ Δ q1 t x τ1 t q2 t x τ2 t 0 on a time scale T, where z t x t p t x τ0 t , 0 < α < γ < β. Our results generalize and improve some known results for oscillation of second-order nonlinear delay dynamic equations on time scales. Some examples are considered to illustrate our main r...

Simple analytical expressions for transparency, threshold, and relaxation oscillation corner frequency are derived for biaxial strain quantum-well lasers. An optimal operating point loss for high speed operation (in the absence of nonlinear gain) is established which varies as the square root of the number of quantum wells. The corresponding relaxation oscillation frequency is found to depend o...

Based on homotopy, which is a basic concept in topology, a general analytic method (namely the homotopy analysis method) is proposed to obtain series solutions of nonlinear differential equations. Different from perturbation techniques, this approach is independent of small/large physical parameters. Besides, different from all previous analytic methods, it provides us with a simple way to adju...

In this article, we study the oscillation of solutions to a nonlinear forced fractional differential equation. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. Based on a transformation of variables and properties of the modified Riemann-liouville derivative, the fractional differential equation is transformed into a second-order ordinary different...

In this paper we establish some new oscillation criteria for a second order nonlinear delay differential equation of Emden–Fowler type with damping term. These results extend and improve some of the well-known results in the nondelay case. Our results in the delay case are new and can be applied to new classes of equations which are not covered by the known criteria for oscillation. Some select...

Abstract: A straightforward method to simulate high–Q quartz crystal oscillator is derived in this paper. The oscillator circuit is expressed under a canonical 5–terminal network which can be easily handled. The oscillator behavior is then described under the form of a nonlinear characteristic polynomial whose coefficients are functions of the circuit components and of the oscillation amplitude...

In this paper, we obtain new oscillation criteria for second-order half-linear impulsive differential equations having fixed moments of impulse actions. We also generalize the results to nonlinear impulsive equations. The oscillation criteria obtained in this paper can be considered as extensions of those given by Leighton, (J. London Math. Soc. 27 (1952)), Coles (Proc. Amer. Math. Soc. 19 (196...

In this paper, by defining a class of functions, we establish some oscillation criteria for the second order nonlinear dynamic equations with forced term x (t) + a(t)f(x(q(t))) = e(t) on a time scale T. Our results unify the oscillation of the second order forced differential equation and the second order forced difference equation. An example is considered to illustrate the main results.

In this paper we shall consider the nonlinear neutral delay differential equations with variable coefficients. Some new sufficient conditions for oscillation of all solutions are obtained. Our results extend and improve some of the well known results in the literature. Some examples are considered to illustrate our main results. The neutral logistic equation with variable coefficients is consid...

This paper is a study of solutions to nonlinear Dirac equations, in domains in Euclidean space, which are generalizations of the Clifford Laplacian as well as elliptic equations in divergence form. A Caccioppoli estimate is used to prove a global integrability theorem for the image of a solution under the Euclidean Dirac operator. Oscillation spaces for Clifford valued functions are used which ...