Existence, uniqueness and stability of solution to mixed integral dynamic systems with instantaneous and noninstantaneous impulses on time scales

2019 ◽  
Vol 359 ◽  
pp. 202-213 ◽  
Author(s):  
Syed Omar Shah ◽  
Akbar Zada
Keyword(s):  
Time Scales ◽  
Dynamic Systems ◽  
Stability Of Solution ◽  
Noninstantaneous Impulses

scholarly journals Lyapunov stability theory for dynamic systems on time scales

1992 ◽  
Vol 5 (3) ◽  
pp. 275-281 ◽  
Author(s):  
Billur Kaymakçalan
Keyword(s):  
Time Scales ◽  
Lyapunov Stability ◽  
Comparison Principle ◽  
Dynamic Systems ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Existence Theory ◽  
Lyapunov’S Second Method ◽  
Stability Results

By use of the necessary calculus and the fundamental existence theory for dynamic systems on time scales, in this paper, we develop Lyapunov's second method in the framework of general comparison principle so that one can cover and include several stability results for both types of equations at the same time.

scholarly journals Stability analysis in terms of two measures for dynamic systems on time scales

1993 ◽  
Vol 6 (4) ◽  
pp. 325-344 ◽  
Author(s):  
Billûr Kaymakçalan
Keyword(s):  
Stability Analysis ◽  
Time Scales ◽  
Dynamic Systems ◽  
Lyapunov’S Second Method ◽  
Two Measures ◽  
Set Up ◽  
Stability Results ◽  
Stability Concepts ◽  
Single Set

Using the theory of Lyapunov's second method developed earlier for time scales, we extend our stability results to two measures which give rise to unification of several stability concepts in a single set up.

scholarly journals Monotone flows and fixed points for dynamic systems on time scales

1994 ◽  
Vol 28 (1-3) ◽  
pp. 185-189 ◽  
Author(s):  
V. Lakshmikantham ◽  
B. Kaymakçalan
Keyword(s):  
Fixed Points ◽  
Time Scales ◽  
Dynamic Systems

scholarly journals On Inequalities of Lyapunov for Two-Dimensional Nonlinear Dynamic Systems on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Qiao-Luan Li ◽  
Wing-Sum Cheung ◽  
Xu-Yang Fu
Keyword(s):  
Time Scales ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Type Equation ◽  
Nonlinear Dynamic Systems ◽  
Two Dimensional

We establish some new Lyapunov-type inequalities for two-dimensional nonlinear dynamic systems on time scales. As for application, boundedness of the Emden-Fowler-type equation is proved.

Monotone solutions of dynamic systems on time scales

2006 ◽  
Vol 12 (3-4) ◽  
pp. 343-355 ◽  
Author(s):  
L. Erbe ◽  
A. Peterson ◽  
C.C. Tisdell
Keyword(s):  
Time Scales ◽  
Dynamic Systems ◽  
Monotone Solutions
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