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 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.

scholarly journals Oscillation criteria of third-order neutral differential equations with damping and distributed deviating arguments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yakun Wang ◽  
Fanwei Meng ◽  
Juan Gu
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Riccati Transformation ◽  
Third Order ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Integral Averaging Technique ◽  
Distributed Deviating Arguments ◽  
Generalized Riccati Transformation

AbstractOur objective in this paper is to study the oscillatory and asymptotic behavior of the solutions of third-order neutral differential equations with damping and distributed deviating arguments. New oscillation criteria are established, which are based on a refinement generalized Riccati transformation. An important tool for this investigation is the integral averaging technique. Moreover, we provide an example to illustrate the main results.

Oscillation Criterion of Third-Order Nonlinear Neutral Damped Functional Differential Equations

2012 ◽  
Vol 204-208 ◽  
pp. 4835-4839
Author(s):  
Yun Hui Zeng
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Oscillation Criterion ◽  
Third Order ◽  
Deviating Arguments ◽  
Integral Averaging Technique ◽  
Generalized Riccati Transformation ◽  
Type Integral ◽  
Functional Differential

In this paper, A class of third-order nonlinear neutral damped functional differential equations with distributed deviating arguments are studied. By using a generalized Riccati transformation and Kamenev-type or Philos-type integral averaging technique,we establish some new sufficient conditions which insure that any solution of this equation oscillates or converges to zero.

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 Oscillation of Solutions to Third-Order Nonlinear Neutral Dynamic Equations on Time Scales

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 86
Author(s):  
Yang-Cong Qiu ◽  
Kuo-Shou Chiu ◽  
Said R. Grace ◽  
Qingmin Liu ◽  
Irena Jadlovská
Keyword(s):  
Time Scales ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Third Order ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Neutral Dynamic Equations ◽  
Oscillation Of Solutions

In this paper, we are concerned with the oscillation of solutions to a class of third-order nonlinear neutral dynamic equations on time scales. New oscillation criteria are presented by employing the Riccati transformation and integral averaging technique. Two examples are shown to illustrate the conclusions.

scholarly journals New Oscillation Criteria for Third-Order Nonlinear Functional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Quanxin Zhang ◽  
Li Gao ◽  
Shouhua Liu ◽  
Yuanhong Yu
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Riccati Transformation ◽  
Third Order ◽  
Nonlinear Functional ◽  
Integral Averaging Technique ◽  
Generalized Riccati Transformation ◽  
Functional Differential

This paper discusses oscillatory and asymptotic behavior of solutions of a class of third-order nonlinear functional differential equations. By using the generalized Riccati transformation and the integral averaging technique, three new sufficient conditions which insure that the solution is oscillatory or converges to zero are established. The results obtained essentially generalize and improve the earlier ones.

scholarly journals Oscillation Criteria for Third-Order Nonlinear Neutral Dynamic Equations with Mixed Deviating Arguments on Time Scales

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 552
Author(s):  
Zhiyu Zhang ◽  
Ruihua Feng ◽  
Irena Jadlovská ◽  
Qingmin Liu
Keyword(s):  
Asymptotic Behavior ◽  
Time Scales ◽  
Dynamic Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Riccati Transformation ◽  
Third Order ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Inequality Technique ◽  
Neutral Dynamic Equations

Under a couple of canonical and mixed canonical-noncanonical conditions, we investigate the oscillation and asymptotic behavior of solutions to a class of third-order nonlinear neutral dynamic equations with mixed deviating arguments on time scales. By means of the double Riccati transformation and the inequality technique, new oscillation criteria are established, which improve and generalize related results in the literature. Several examples are given to illustrate the main results.

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