scholarly journals Some Delay Integral Inequalities on Time Scales and Their Applications in the Theory of Dynamic Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
Qinghua Feng ◽  
Fanwei Meng ◽  
Yaoming Zhang ◽  
Jinchuan Zhou ◽  
Bin Zheng
Keyword(s):  
Time Scales ◽  
The Other ◽  
Integral Inequalities ◽  
Dynamic Equations ◽  
Other Hand ◽  
Delay Dynamic Equations ◽  
Quantitative Properties

We establish some delay integral inequalities on time scales, which on one hand provide a handy tool in the study of qualitative as well as quantitative properties of solutions of certain delay dynamic equations on time scales and on the other hand unify some known continuous and discrete results in the literature.

scholarly journals Explicit Bounds to Some New Gronwall-Bellman-Type Delay Integral Inequalities in Two Independent Variables on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-25 ◽  
Author(s):  
Fanwei Meng ◽  
Qinghua Feng ◽  
Bin Zheng
Keyword(s):  
Time Scales ◽  
Integral Inequalities ◽  
Dynamic Equations ◽  
Qualitative And Quantitative ◽  
Independent Variables ◽  
Delay Dynamic Equations ◽  
Explicit Bounds ◽  
Quantitative Properties ◽  
Two Independent Variables

Some new Gronwall-Bellman-type delay integral inequalities in two independent variables on time scales are established, which provide a handy tool in the research of qualitative and quantitative properties of solutions of delay dynamic equations on time scales. The established inequalities generalize some of the results in the work of Zhang and Meng 2008, Pachpatte 2002, and Ma 2010.

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 Bounds of Double Integral Dynamic Inequalities in Two Independent Variables on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
S. H. Saker
Keyword(s):  
Time Scales ◽  
Unknown Function ◽  
The Other ◽  
Dynamic Equations ◽  
Double Integral ◽  
Independent Variables ◽  
Explicit Bounds ◽  
Quantitative Properties ◽  
The One ◽  
Two Independent Variables

Our aim in this paper is to establish some explicit bounds of the unknown function in a certain class of nonlinear dynamic inequalities in two independent variables on time scales which are unbounded above. These on the one hand generalize and on the other hand furnish a handy tool for the study of qualitative as well as quantitative properties of solutions of partial dynamic equations on time scales. Some examples are considered to demonstrate the applications of the results.

scholarly journals Some New Delay Integral Inequalities in Two Independent Variables on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-18
Author(s):  
Bin Zheng ◽  
Yaoming Zhang ◽  
Qinghua Feng
Keyword(s):  
Time Scales ◽  
Integral Inequalities ◽  
Dynamic Equations ◽  
Boundedness Of Solutions ◽  
Independent Variables ◽  
Discrete Analysis ◽  
Delay Dynamic Equations ◽  
Two Independent Variables

Some new Gronwall-Bellman-type delay integral inequalities in two independent variables on time scales are established, which can be used as a handy tool in the research of boundedness of solutions of delay dynamic equations on time scales. Some of the established results are 2D extensions of several known results in the literature, while some results unify existing continuous and discrete analysis.

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 Some Nonlinear Delay Volterra–Fredholm Type Dynamic Integral Inequalities on Time Scales

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Yazhou Tian ◽  
A. A. El-Deeb ◽  
Fanwei Meng
Keyword(s):  
Time Scales ◽  
Qualitative Theory ◽  
Integral Inequalities ◽  
Dynamic Equations ◽  
Fredholm Type ◽  
Explicit Bounds ◽  
Theoretical Results ◽  
Nonlinear Delay

We are devoted to studying a class of nonlinear delay Volterra–Fredholm type dynamic integral inequalities on time scales, which can provide explicit bounds on unknown functions. The obtained results can be utilized to investigate the qualitative theory of nonlinear delay Volterra–Fredholm type dynamic equations. An example is also presented to illustrate the theoretical results.

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