scholarly journals Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales

2005 ◽  
Vol 181 (1) ◽  
pp. 92-102 ◽  
Author(s):  
L. Erbe ◽  
A. Peterson ◽  
S.H. Saker
Keyword(s):  
Asymptotic Behavior ◽  
Time Scales ◽  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Asymptotic Behavior Of Solutions ◽  
Third Order ◽  
Nonlinear Dynamic Equation

scholarly journals Oscillation Criteria of Singular Initial-Value Problem for Second Order Nonlinear Dynamic Equation on Time Scales

2018 ◽  
Vol 5 (1) ◽  
pp. 102-112 ◽  
Author(s):  
Shekhar Singh Negi ◽  
Syed Abbas ◽  
Muslim Malik
Keyword(s):  
Time Scales ◽  
Initial Value Problem ◽  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Type Inequality ◽  
Second Order ◽  
Oscillation Criterion ◽  
Initial Value ◽  
Nonlinear Dynamic Equation ◽  
Singular Initial Value Problem

AbstractBy using of generalized Opial’s type inequality on time scales, a new oscillation criterion is given for a singular initial-value problem of second-order dynamic equation on time scales. Some oscillatory results of its generalizations are also presented. Example with various time scales is given to illustrate the analytical findings.

scholarly journals On Hyers–Ulam and Hyers–Ulam–Rassias Stability of a Nonlinear Second-Order Dynamic Equation on Time Scales

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1507
Author(s):  
Alaa E. Hamza ◽  
Maryam A. Alghamdi ◽  
Mymonah S. Alharbi
Keyword(s):  
Time Scales ◽  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Sufficient Conditions ◽  
Second Order ◽  
Nonlinear Dynamic Equation ◽  
Theoretical Results ◽  
Rassias Stability

In this paper, we obtain sufficient conditions for Hyers–Ulam and Hyers–Ulam–Rassias stability of an abstract second–order nonlinear dynamic equation on bounded time scales. An illustrative example is given to show the applicability of the theoretical results.

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.

scholarly journals Oscillation Behavior of a Class of Second-Order Dynamic Equations with Damping on Time Scales

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Weisong Chen ◽  
Zhenlai Han ◽  
Shurong Sun ◽  
Tongxing Li
Keyword(s):  
Time Scales ◽  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Second Order ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Nonlinear Dynamic Equation ◽  
Oscillation Theorems

By using a Riccati transformation and inequality, we present some new oscillation theorems for the second-order nonlinear dynamic equation with damping on time scales. An example illustrating the importance of our results is also included.

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 of Second-Order Dynamic Equations on Time Scales

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1867
Author(s):  
Ya-Ru Zhu ◽  
Zhong-Xuan Mao ◽  
Shi-Pu Liu ◽  
Jing-Feng Tian
Keyword(s):  
Time Scales ◽  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Second Order ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Scaling Technique ◽  
Oscillation Criteria ◽  
Nonlinear Dynamic Equation ◽  
Generalized Riccati Transformation

In this paper, we consider the oscillation behavior of the following second-order nonlinear dynamic equation. λ(s)Ψ1φΔ(s)y(φ(s))ΔΔ+η(s)Φ(y(τ(s)))=0,s∈[s0,∞)T. By employing generalized Riccati transformation and inequality scaling technique, we establish some oscillation criteria.

Sign in / Sign up

Export Citation Format

Share Document