scholarly journals Existence and Asymptotic Behaviors of Nonoscillatory Solutions of Third Order Time Scale Systems

2020 ◽  
Author(s):  
Özkan Öztürk
Keyword(s):  
Time Scales ◽  
Asymptotic Properties ◽  
Three Dimensional ◽  
Optimization Theory ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
Main Method ◽  
Asymptotic Behaviors ◽  
Improper Integrals ◽  
And Robotics

Nonoscillation theory with asymptotic behaviors takes a significant role for the theory of three-dimensional (3D) systems dynamic equations on time scales in order to have information about the asymptotic properties of such solutions. Some applications of such systems in discrete and continuous cases arise in control theory, optimization theory, and robotics. We consider a third order dynamical systems on time scales and investigate the existence of nonoscillatory solutions and asymptotic behaviors of such solutions. Our main method is to use some well-known fixed point theorems and double/triple improper integrals by using the sign of solutions. We also provide examples on time scales to validate our theoretical claims.

Asymptotic properties of third order functional dynamic equations on time scales

2011 ◽  
Vol 100 (3) ◽  
pp. 203-222 ◽  
Author(s):  
I. Kubiaczyk ◽  
S. H. Saker
Keyword(s):  
Time Scales ◽  
Asymptotic Properties ◽  
Dynamic Equations ◽  
Third Order

scholarly journals Oscillatory and Asymptotic Properties on a Class of Third Nonlinear Dynamic Equations with Damping Term on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-17
Author(s):  
Qinghua Feng ◽  
Huizeng Qin
Keyword(s):  
Time Scales ◽  
Nonlinear Dynamic ◽  
Asymptotic Properties ◽  
The Other ◽  
Dynamic Equations ◽  
Damping Term ◽  
Third Order ◽  
Discrete Analysis ◽  
Other Hand ◽  
Nonlinear Dynamic Equations

We establish some new oscillatory and asymptotic criteria for a class of third-order nonlinear dynamic equations with damping term on time scales. The established results on one hand extend some known results in the literature on the other hand unify continuous and discrete analysis. For illustrating the validity of the established results, we also present some applications for them.

scholarly journals Existence of nonoscillatory solutions to nonlinear third-order neutral dynamic equations on time scales

2017 ◽  
Vol 10 (08) ◽  
pp. 4352-4363 ◽  
Author(s):  
Yang-Cong Qiu ◽  
Akbar Zada ◽  
Shuhong Tang ◽  
Tongxing Li
Keyword(s):  
Time Scales ◽  
Dynamic Equations ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
Neutral Dynamic Equations

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 for Third-Order Nonlinear Differential Equations with Deviating Argument

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Miroslav Bartušek ◽  
Mariella Cecchi ◽  
Zuzana Došlá ◽  
Mauro Marini
Keyword(s):  
Nonlinear Differential Equations ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Nonlinear Ordinary Differential Equation ◽  
Damping Term ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
Deviating Argument ◽  
The Third ◽  
Necessary And Sufficient

We study necessary and sufficient conditions for the oscillation of the third-order nonlinear ordinary differential equation with damping term and deviating argumentx‴(t)+q(t)x′(t)+r(t)f(x(φ(t)))=0. Motivated by the work of Kiguradze (1992), the existence and asymptotic properties of nonoscillatory solutions are investigated in case when the differential operatorℒx=x‴+q(t)x′is oscillatory.

scholarly journals Existence of nonoscillatory solutions tending to zero of third-order neutral dynamic equations on time scales

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yang-Cong Qiu ◽  
Irena Jadlovská ◽  
Kuo-Shou Chiu ◽  
Tongxing Li
Keyword(s):  
Time Scales ◽  
Dynamic Equations ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
Neutral Dynamic Equations

scholarly journals Asymptotic Properties of Third-Order Nonlinear Differential Equations

2013 ◽  
Vol 54 (1) ◽  
pp. 19-29
Author(s):  
Blanka Baculíková ◽  
Jozef Džurina
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equations ◽  
Asymptotic Properties ◽  
Comparison Theorems ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
Advanced Case ◽  
The Third ◽  
Functional Differential ◽  
New Criteria

Abstract We present new criteria guaranteeing that all nonoscillatory solutions of the third-order functional differential equation tend to zero. Our results are based on the suitable comparison theorems. We consider both delay and advanced case of studied equation. The results obtained essentially improve and complement earlier ones.

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