Sentence examples for behavior of the equation from inspiring English sources
The first one describes the asymptotic behavior of the equation.
The behavior of the equation is systematically explored and illustrated through numerical results.
To the best of author's knowledge, nothing is known regarding the oscillatory behavior of the equation, so this article initiates the study.
By discussing the signs of ith-order derivatives of eventually positive solutions, for (i=1,ldots,n-1), and using the generalized Riccati technique and integral averaging technique, we derive new criteria for oscillation and asymptotic behavior of the equation.
Qi and Huang [26] studied the oscillation behavior of the equation of the form ( a ( t ) [ r ( t ) D − α x ( t ) ] ′ ) ′ + p ( t ) [ r ( t ) D − α x ( t ) ] ′ − q ( t ) ∫ t ∞ ( ξ − t ) − α x d ξ = 0, t ∈ [ t 0, ∞ ), where D − α x ( t ) also denotes the Liouville right-sided fractional derivative and some sufficient conditions for the oscillation of the equation have been given.
We can use this freedom to simplify the equation and reveal what the important parameters are that govern the behavior of the equation.
The model formulation was slightly modified, and the way to determine a crucial parameter was changed, revealing a previously unexplored behavior of the equations.
To evaluate the long term behavior of the equations, a simulation model was constructed by linking all of the component equations and using them to project each plot from its initial to final measurement.
When f ≠ 0, Qin and Zhao [16] proved the global existence and asymptotic behavior for γ = 1 and μ = const with boundary conditions u 0,t) = u(1,t) = 0; Zhang and Fang [17] established the global behavior of the Equations (1.1 - 1.2 1.1 - 1.2ndary conditions u(0,t) = ρ(1,t) = 0.
Monte Carlo simulations of the behavior of this equation were obtained using the publicly available software MesoRD 0.2.0 [ 33].
The results on the dynamics behavior of this equation and its modifications are abundant [3 21] and systematically collected and compared by Berezansky et al. [22].
