Oscillation Theorems for Perturbed Second Order Nonlinear Differential Equations with Damping

Some oscillation criteria for solutions of a general perturbed second order ordinary differential equation with damping (r(t)x′ (t))′ + h(t)f (x)x′ (t) + ψ(t, x) = H(t, x(t), x′ (t)) with alternating coefficients are given. The results obtained improve and extend some existing results in the literature

Oscillation Theorems for Second Order Sublinear Ordinary Differential Equations

Oscillation criteria are given for the second order sublinear non-autonomous differential equation. (r(t) (x)x′(t))′ + q(t)g(x(t)) = (t). These criteria extends and improves earlier oscillation criteria of Kamenev, Kura, Philos and Wong. Oscillation criteria are also given for second order sublinear damped non-autonomous differential equations

Oscillation Criteria for First Order Delay Differential Equations

2000 Mathematics Subject Classification: 34K15.This paper is concerned with the oscillatory behavior of first-order delay differential equation of the form x'(t) + p(t)x (τ(t)) = 0

Oscillation Criteria for Nonlinear Differential Equations of Second Order with Damping Term

2000 Mathematics Subject Classification: 34C10, 34C15.Some new criteria for the oscillation of all solutions of second order differential equations of the form (d/dt)(r(t)ψ(x)|dx/dt|α−2(dx/dt))+ p(t)φ(|x|α−2x,r(t) ψ(x)|dx/dt|α−2(dx/dt))+q(t)|x|α−2 x=0, and the more general equation (d/dt)(r(t)ψ(x)|dx/dt|α−2(dx/dt))+p(t)φ(g(x),r(t) ψ(x)|dx/dt|α−2 (dx/dt))+q(t)g(x)=0, are established. our results generalize and extend some known oscillation criterain in the literature

Oscillation of Nonlinear Neutral Delay Differential Equations

2000 Mathematics Subject Classification: 34K15, 34C10.In this paper, we study the oscillatory behavior of first order nonlinear neutral delay differential equation (x(t) − q(t) x(t − σ(t))) ′ +f(t,x( t − τ(t))) = 0, where σ, τ ∈ C([t0,∞),(0,∞)), q О C([t0,∞), [0,∞)) and f ∈ C([t0,∞) ×R,R). The obtained results extended and improve several of the well known previously results in the literature. Our results are illustrated with an example

Necessary and Sufficient Condition for Oscillations of Neutral Differential Equation

2000 Mathematics Subject Classification: 34K15, 34C10.We obtain necessary and sufficient conditions for the oscillation of all solutions of neutral differential equation with mixed (delayed and advanced) arguments ..

ASYMPTOTIC BEHAVIOR OF TWO DIMENSIONAL RATIONAL SYSTEM OF DIFFERENCE EQUATIONS

Abstract. In this paper, we investigate global behavior of the system of two nonlinear difference equations where a 1 , a 2 , a 3 , b 1 , b 2 , b 3 , r ∈ (0, ∞) and the initial conditions x 0 , y 0 ∈ (0, ∞). Some numerical examples are given to illustrate our results

Routh-Hurwitz Stability and Quasiperiodic Attractors in a Fractional-Order Model for Awareness Programs: Applications to COVID-19 Pandemic

This work explores Routh-Hurwitz stability and complex dynamics in models for awareness programs to mitigate the spread of epidemics. Here, the investigated models are the integer-order model for awareness programs and their corresponding fractional form. A non-negative solution is shown to exist inside the globally attracting set (GAS) of the fractional model. It is also shown that the diseasefree steady state is locally asymptotically stable (LAS) given that R0 is less than one, where R0 is the basic reproduction number. However, as R0>1, an endemic steady state is created whose stability analysis is studied according to the extended fractional Routh-Hurwitz scheme, as the order lies in the interval (0,2]. Furthermore, the proposed awareness program models are numerically simulated based on the predictor-corrector algorithm and some clinical data of the COVID-19 pandemic in KSA. Besides, the model's basic reproduction number in KSA is calculated using the selected data R0=1.977828168. In conclusion, the findings indicate the effectiveness of fractional-order calculus to simulate, predict, and control the spread of epidemiological diseases. © 2022 Taher S. Hassan et al