scholarly journals Oscillation behavior of third-order quasilinear neutral delay dynamic equations on time scales

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1425-1436 ◽  
Author(s):  
Nadide Utku ◽  
Mehmet Şenel
Keyword(s):  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Neutral Delay ◽  
Third Order ◽  
The Third ◽  
Delay Dynamic Equation ◽  
Integral Averaging Technique ◽  
Neutral Delay Dynamic Equation ◽  
Generalized Riccati Transformation ◽  
Delay Dynamic Equations

The aim of this paper is to give oscillation criteria for the third-order quasilinear neutral delay dynamic equation [r(t)([x(t)+ p(t)x(?0(t))]??)?]? + q1(t)x?(?1(t)) + q2(t)x?(?2(t)) = 0; on a time scale T, where 0 < ? < ? < ?. By using a generalized Riccati transformation and integral averaging technique, we establish some new sufficient conditions which ensure that every solution of this equation oscillates or converges to zero.

Oscillation for Third-Order Nonlinear Delay Dynamic Equations on Time Scales

2013 ◽  
Vol 475-476 ◽  
pp. 1578-1582
Author(s):  
Shou Hua Liu ◽  
Quan Xin Zhang ◽  
Li Gao
Keyword(s):  
Time Scales ◽  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Neutral Delay ◽  
Third Order ◽  
Generalized Riccati Transformation ◽  
Delay Dynamic Equations ◽  
Inequality Technique ◽  
Nonlinear Delay

The oscillation for certain third-order nonlinear neutral delay dynamic equations on time scales is discussed in this article. By using the generalized Riccati transformation and the inequality technique, three new different sufficient conditions which ensure that every solution is oscillatory or converges to zero are established. The results obtained essentially generalize and improve earlier ones.

scholarly journals New Oscillatory Behavior of Third-Order Nonlinear Delay Dynamic Equations on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Li Gao ◽  
Quanxin Zhang ◽  
Shouhua Liu
Keyword(s):  
Time Scales ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Third Order ◽  
Generalized Riccati Transformation ◽  
Delay Dynamic Equations ◽  
Inequality Technique ◽  
Nonlinear Delay

A class of third-order nonlinear delay dynamic equations on time scales is studied. By using the generalized Riccati transformation and the inequality technique, four new sufficient conditions which ensure that every solution is oscillatory or converges to zero are established. The results obtained essentially improve earlier ones. Some examples are considered to illustrate the main results.

scholarly journals On the Oscillation of Second Order Nonlinear Neutral Delay Dynamic Equations

2007 ◽  
Vol 14 (4) ◽  
pp. 597-606
Author(s):  
Hassan A. Agwo
Keyword(s):  
Dynamic Equation ◽  
Time Scale ◽  
Second Order ◽  
Dynamic Equations ◽  
Sufficient Condition ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Delay Dynamic Equation ◽  
Neutral Delay Dynamic Equation ◽  
Delay Dynamic Equations

Abstract In this paper we obtain some new oscillation criteria for the second order nonlinear neutral delay dynamic equation (𝑥(𝑡) – 𝑝(𝑡)𝑥(𝑡 – τ 1))ΔΔ + 𝑞(𝑡)𝑓(𝑥(𝑡 – τ 2)) = 0, on a time scale 𝕋. Moreover, a new sufficient condition for the oscillation sublinear equation (𝑥(𝑡) – 𝑝(𝑡)𝑥(𝑡 – τ 1))″ + 𝑞(𝑡)𝑓(𝑥(𝑡 – τ 2)) = 0, is presented, which improves other conditions and an example is given to illustrate our result.

scholarly journals Oscillation behavior of third-order nonlinear neutral dynamic equations on time scales with distributed deviating arguments

Filomat ◽  
2014 ◽  
Vol 28 (6) ◽  
pp. 1211-1223 ◽  
Author(s):  
Tamer Şenel ◽  
Nadide Utku
Keyword(s):  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Third Order ◽  
Deviating Arguments ◽  
Integral Averaging Technique ◽  
Distributed Deviating Arguments ◽  
Generalized Riccati Transformation ◽  
Positive Functions ◽  
Positive Integers ◽  
Neutral Dynamic Equations

The aim of this paper is to give oscillation criteria for the third-order neutral dynamic equations with distributed deviating arguments of the form [r(t)([x(t)+p(t)x(?(t))]??)?]? + ?dc f(t,x[?(t,?)])?? = 0; where ?>0 is the quotient of odd positive integers with r(t) and p(t) real-valued rd-continuous positive functions defined on T. By using a generalized Riccati transformation and integral averaging technique, we establish some new sufficient conditions which ensure that every solution of this equation oscillates or converges to zero.

scholarly journals Oscillation Theorems for Second-Order Half-Linear Neutral Delay Dynamic Equations with Damping on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Quanxin Zhang ◽  
Shouhua Liu
Keyword(s):  
Time Scales ◽  
Second Order ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation ◽  
Delay Dynamic Equations ◽  
Inequality Technique ◽  
Oscillation Theorems

We establish the oscillation criteria of Philos type for second-order half-linear neutral delay dynamic equations with damping on time scales by the generalized Riccati transformation and inequality technique. Our results are new even in the continuous and the discrete cases.

scholarly journals Oscillatory behaviour of higher-order nonlinear neutral delay dynamic equations on time scales

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2635-2649
Author(s):  
M.M.A. El-Sheikh ◽  
M.H. Abdalla ◽  
A.M. Hassan
Keyword(s):  
Sufficient Conditions ◽  
Higher Order ◽  
Comparison Theorems ◽  
Dynamic Equations ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
Riccati Technique ◽  
Delay Dynamic Equations ◽  
Positive Integers ◽  
Oscillation Of Solutions

In this paper, new sufficient conditions are established for the oscillation of solutions of the higher order dynamic equations [r(t)(z?n-1(t))?]? + q(t) f(x(?(t)))=0, for t ?[t0,?)T, where z(t):= x(t)+ p(t)x(?(t)), n ? 2 is an even integer and ? ? 1 is a quotient of odd positive integers. Under less restrictive assumptions for the neutral coefficient, we employ new comparison theorems and Generalized Riccati technique.

scholarly journals Existence of nonoscillatory solutions to third order nonlinear neutral difference equations

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 4981-4991
Author(s):  
K.S. Vidhyaa ◽  
C. Dharuman ◽  
John Graef ◽  
E. Thandapani
Keyword(s):  
Fixed Point ◽  
Sufficient Conditions ◽  
Delay Difference Equation ◽  
Neutral Delay ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
Neutral Difference Equations ◽  
Positive And Negative Coefficients ◽  
The Third ◽  
Delay Difference

The authors consider the third order neutral delay difference equation with positive and negative coefficients ?(an?(bn?(xn + pxn-m)))+pnf(xn-k)- qn1(xn-l) = 0, n ? n0, and give some new sufficient conditions for the existence of nonoscillatory solutions. Banach?s fixed point theorem plays a major role in the proofs. Examples are provided to illustrate their main results.

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