Forced oscillation of second-order neutral equations

2000 ◽  
Vol 21 (10) ◽  
pp. 1197-1200
Author(s):  
Wang Pei-guang ◽  
GE Wei-gao
Keyword(s):  
Forced Oscillation ◽  
Second Order ◽  
Neutral Equations

scholarly journals Non-Linear Neutral Differential Equations with Damping: Oscillation of Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 285
Author(s):  
Saad Althobati ◽  
Jehad Alzabut ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Order Equation ◽  
Second Order ◽  
Riccati Technique ◽  
Neutral Equations ◽  
Neutral Differential Equations ◽  
Main Equation ◽  
Non Linear ◽  
Even Order

The oscillation of non-linear neutral equations contributes to many applications, such as torsional oscillations, which have been observed during earthquakes. These oscillations are generally caused by the asymmetry of the structures. The objective of this work is to establish new oscillation criteria for a class of nonlinear even-order differential equations with damping. We employ different approach based on using Riccati technique to reduce the main equation into a second order equation and then comparing with a second order equation whose oscillatory behavior is known. The new conditions complement several results in the literature. Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples.

Forced oscillation of second order superlinear differential equations

2005 ◽  
Vol 278 (12-13) ◽  
pp. 1621-1628 ◽  
Author(s):  
Yuan Gong Sun ◽  
James S. W. Wong
Keyword(s):  
Differential Equations ◽  
Forced Oscillation ◽  
Second Order

scholarly journals Forced Oscillation of Second-Order Half-Linear Dynamic Equations on Time Scales

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Quanwen Lin ◽  
Baoguo Jia ◽  
Qiru Wang
Keyword(s):  
Dynamic Equation ◽  
Forced Oscillation ◽  
Second Order ◽  
Oscillation Criterion ◽  
Linear Dynamic ◽  
Oscillation Result ◽  
Condition Of Oscillation ◽  
Interval Oscillation ◽  
Linear Differential ◽  
Positive Integers

We will establish a new interval oscillation criterion for second-order half-linear dynamic equation(r(t)[xΔ(t)]α)Δ+p(t)xα(σ(t))=f(t)on a time scaleTwhich is unbounded, which is a extension of the oscillation result for second order linear dynamic equation established by Erbe et al. (2008). As an application, we obtain a sufficient condition of oscillation of the second-order half-linear differential equation([x′(t)]α)′+csintxα(t)=cos⁡t, whereα=p/q,p,qare odd positive integers.

Oscillations of Second Order Neutral Equations

1988 ◽  
Vol 40 (6) ◽  
pp. 1301-1314 ◽  
Author(s):  
G. Ladas ◽  
E. C. Partheniadis ◽  
Y. G. Sficas
Keyword(s):  
Second Order ◽  
List Type ◽  
Necessary And Sufficient Condition ◽  
Real Numbers ◽  
Neutral Equations ◽  
Deviating Arguments ◽  
Real Roots ◽  
All Solutions ◽  
Image Position ◽  
Necessary And Sufficient

Consider the second order neutral differential equation1where the coefficients p and q and the deviating arguments τ and σ are real numbers. The characteristic equation of Eq. (1) is2The main result in this paper is the following necessary and sufficient condition for all solutions of Eq. (1) to oscillate.THEOREM. The following statements are equivalent:(a) Every solution of Eq. (1) oscillates.(b) Equation (2) has no real roots.

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