scholarly journals Asymptotics and Hille-Type Results for Dynamic Equations of Third Order with Deviating Arguments

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2007
Author(s):  
Taher S. Hassan ◽  
A. Othman Almatroud ◽  
Mohammed M. Al-Sawalha ◽  
Ismoil Odinaev
Keyword(s):  
Time Scales ◽  
Oscillation Criterion ◽  
Dynamic Equations ◽  
Qualitative Behavior ◽  
Sufficient Condition ◽  
Dynamical Equations ◽  
Third Order ◽  
Deviating Arguments ◽  
All Solutions ◽  
Type Oscillation

The aim of this paper is to deduce the asymptotic and Hille-type criteria of the dynamic equations of third order on time scales. Some of the presented results concern the sufficient condition for the oscillation of all solutions of third-order dynamical equations. Additionally, compared with the related contributions reported in the literature, the Hille-type oscillation criterion which is derived is superior for dynamic equations of third order. The symmetry plays a positive and influential role in determining the appropriate type of study for the qualitative behavior of solutions to dynamic equations. Some examples of Euler-type equations are included to demonstrate the finding.

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.

Asymptotic behavior of solutions of forced third-order dynamic equations

Analysis ◽  
2019 ◽  
Vol 39 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Martin Bohner ◽  
Said R. Grace ◽  
Irena Jadlovská
Keyword(s):  
Asymptotic Behavior ◽  
Time Scales ◽  
Dynamic Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Nonlinear Functions ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
All Solutions

Abstract This paper deals with asymptotic behavior of nonoscillatory solutions of certain third-order forced dynamic equations on time scales. The main goal is to investigate when all solutions behave at infinity like certain nontrivial nonlinear functions.

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

2014 ◽  
Vol 61 (1) ◽  
pp. 141-161 ◽  
Author(s):  
Taher S. Hassan ◽  
Said R. Grace
Keyword(s):  
Time Scales ◽  
Nonlinear Dynamic ◽  
Dynamic Equations ◽  
Third Order ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Distributed Deviating Arguments ◽  
Nonlinear Dynamic Equations

Abstract Some new oscillation criteria for third order neutral nonlinear dynamic equations with distributed deviating arguments on time scales are established. The obtained results extend, improve and correlate many known oscillation results for third order dynamic equations

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.

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