Lyapunov stability for measure differential equations and dynamic equations on time scales

2019 ◽  
Vol 267 (7) ◽  
pp. 4192-4223 ◽  
Author(s):  
M. Federson ◽  
R. Grau ◽  
J.G. Mesquita ◽  
E. Toon
Keyword(s):  
Differential Equations ◽  
Time Scales ◽  
Lyapunov Stability ◽  
Dynamic Equations

scholarly journals Li–Yorke Chaos in Hybrid Systems on a Time Scale

2015 ◽  
Vol 25 (14) ◽  
pp. 1540024 ◽  
Author(s):  
Marat Akhmet ◽  
Mehmet Onur Fen
Keyword(s):  
Differential Equations ◽  
Hybrid Systems ◽  
Time Scales ◽  
Time Scale ◽  
Impulsive Differential Equations ◽  
Reduction Technique ◽  
Duffing Equation ◽  
Dynamic Equations ◽  
Definition Of ◽  
First Time

By using the reduction technique to impulsive differential equations [Akhmet & Turan, 2006], we rigorously prove the presence of chaos in dynamic equations on time scales (DETS). The results of the present study are based on the Li–Yorke definition of chaos. This is the first time in the literature that chaos is obtained for DETS. An illustrative example is presented by means of a Duffing equation on a time scale.

scholarly journals Solvability and Stability of Impulsive Set Dynamic Equations on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Shihuang Hong ◽  
Jing Gao ◽  
Yingzi Peng
Keyword(s):  
Differential Equations ◽  
Time Scales ◽  
Difference Equations ◽  
Time Scale ◽  
Dynamic Equations ◽  
Stability Of Solutions ◽  
Real Numbers ◽  
Generalized Derivative ◽  
Special Cases ◽  
Existence And Stability

A class of new nonlinear impulsive set dynamic equations is considered based on a new generalized derivative of set-valued functions developed on time scales in this paper. Some novel criteria are established for the existence and stability of solutions of such model. The approaches generalize and incorporate as special cases many known results for set (or fuzzy) differential equations and difference equations when the time scale is the set of the real numbers or the integers, respectively. Finally, some examples show the applicability of our results.

scholarly journals Lyapunov Stability of Quasilinear Implicit Dynamic Equations on Time Scales

2011 ◽  
Vol 2011 (1) ◽  
pp. 979705 ◽  
Author(s):  
NH Du ◽  
NC Liem ◽  
CJ Chyan ◽  
SW Lin
Keyword(s):  
Time Scales ◽  
Lyapunov Stability ◽  
Dynamic Equations

Growth of solutions for measure differential equations and dynamic equations on time scales

2019 ◽  
Vol 479 (1) ◽  
pp. 941-962
Author(s):  
Claudio A. Gallegos ◽  
Hernán R. Henríquez ◽  
Jaqueline G. Mesquita
Keyword(s):  
Differential Equations ◽  
Time Scales ◽  
Dynamic Equations ◽  
Growth Of Solutions

scholarly journals THREE POSITIVE PERIODIC SOLUTIONS FOR DYNAMIC EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT AND IMPULSE ON TIME SCALES

2010 ◽  
Vol 53 (2) ◽  
pp. 369-377 ◽  
Author(s):  
YONGKUN LI ◽  
ERLIANG XU
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Time Scales ◽  
Dynamic Equations ◽  
Positive Periodic Solutions ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Constant Argument

AbstractIn this paper, by using the Leggett–Williams fixed point theorem, the existence of three positive periodic solutions for differential equations with piecewise constant argument and impulse on time scales is investigated. Some easily verifiable sufficient criteria are established. Finally, an example is given to illustrate the results.

Theory and applications of first-order systems of Stieltjes differential equations

2017 ◽  
Vol 6 (1) ◽  
pp. 13-36 ◽  
Author(s):  
Marlène Frigon ◽  
Rodrigo López Pouso
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Time Scales ◽  
Existence And Uniqueness ◽  
Basic Theory ◽  
Dynamic Equations ◽  
Uniqueness Of Solutions ◽  
First Order ◽  
Systems Of Differential Equations ◽  
Set Up

AbstractWe set up the basic theory of existence and uniqueness of solutions for systems of differential equations with usual derivatives replaced by Stieltjes derivatives. This type of equations contains as particular cases dynamic equations on time scales and impulsive ordinary differential equations.

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