Theory of Differential and Integral Inequalities with Initial Time Difference and Applications

1999 ◽  
pp. 191-203 ◽  
Author(s):  
V. Lakshmikantham ◽  
A. S. Vatsala
Keyword(s):  
Time Difference ◽  
Integral Inequalities ◽  
Initial Time

scholarly journals Initial Time Difference Stability of Causal Differential Systems in terms of Lyapunov Functions and Lyapunov Functionals

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Coşkun Yakar ◽  
Mustafa Bayram Gücen
Keyword(s):  
Differential System ◽  
Lyapunov Functions ◽  
Lyapunov Functional ◽  
Initial Position ◽  
Time Difference ◽  
Initial Time ◽  
Qualitative Behavior ◽  
Lyapunov Functionals ◽  
Comparison Result ◽  
Differential Systems

We investigate the qualitative behavior of a perturbed causal differential equation that differs in initial position and initial time with respect to the unperturbed causal differential equations. We compare the classical notion of stability of the causal differential systems to the notion of initial time difference stability of causal differential systems and present a comparison result in terms of Lyapunov functions. We have utilized Lyapunov functions and Lyapunov functional in the study of stability theory of causal differential systems when establishing initial time difference stability of the perturbed causal differential system with respect to the unperturbed causal differential system.

scholarly journals Monotone iterative technique by upper and lower solutions with initial time difference

2015 ◽  
Vol 16 (1) ◽  
pp. 575
Author(s):  
Coşkun Yakar ◽  
Ismet Arslan ◽  
Muhammed Çiçek
Keyword(s):  
Upper And Lower Solutions ◽  
Monotone Iterative Technique ◽  
Time Difference ◽  
Initial Time ◽  
Iterative Technique ◽  
Monotone Iterative

scholarly journals Systems of Differential Inequalities with Initial Time Difference

2004 ◽  
Vol 56 (1) ◽  
pp. 173-182 ◽  
Author(s):  
T. Jankowski
Keyword(s):  
Time Difference ◽  
Initial Time ◽  
Differential Inequalities
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