scholarly journals Nonlinear Dynamical Integral Inequalities in Two Independent Variables and Their Applications

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Yuangong Sun
Keyword(s):  
Dynamical Systems ◽  
Time Scales ◽  
Integral Inequalities ◽  
Jump Operator ◽  
Qualitative Properties ◽  
Nonlinear Dynamical ◽  
Independent Variables ◽  
Explicit Bounds ◽  
Qualitative Properties Of Solutions ◽  
Two Independent Variables

In this paper, we investigate some nonlinear dynamical integral inequalities involving the forward jump operator in two independent variables. These inequalities provide explicit bounds on unknown functions, which can be used as handy tools to study the qualitative properties of solutions of certain partial dynamical systems on time scales pairs.

scholarly journals A Generalization of Linear and Nonlinear Retarded Integral Inequalities in Two Independent Variables

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Ying Jiang ◽  
Guojing Xing ◽  
Chenghui Zhang
Keyword(s):  
Integral Inequalities ◽  
Qualitative Properties ◽  
Analysis Techniques ◽  
Independent Variables ◽  
Amplification Method ◽  
Paper Work ◽  
Explicit Bounds ◽  
Linear And Nonlinear ◽  
Qualitative Properties Of Solutions ◽  
Two Independent Variables

Integral inequalities, which provide explicit bounds on unknown functions, are used to serve as handy tools in the study of the qualitative properties of solutions to differential and integral equations. By utilizing some analysis techniques, such as amplification method, differential, and integration, several new types of linear and nonlinear retarded integral inequalities in two independent variables are provided. These results generalize and complement previous ones. An illustrative example is given to support the obtained results. The study of the numerical example shows that the new results presented in this paper work well in the analysis of retarded integral inequalities in two independent variables.

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 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 ON SOME NEW GENERALIZATIONS OF CERTAIN GAMIDOV INTEGRAL INEQUALITIES IN TWO INDEPENDENT VARIABLES AND THEIR APPLICATIONS

2018 ◽  
pp. 467
Author(s):  
Khaled Boukerrioua ◽  
Dallel Diabi ◽  
Brahim Kilani
Keyword(s):  
Integral Inequalities ◽  
Independent Variables ◽  
Type Integral ◽  
Explicit Bounds ◽  
Two Independent Variables

The goal of this paper is to derive some new generalizations of certain Gamidov type integral inequalities in two variables which provide explicit bounds on unknown functions. To show the feasibility of the obtained inequalities,some illustrative examples are also introduce.

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