Existence of a solution of a class of multivalued differential equations with deviating argument

1979 ◽  
Vol 30 (5) ◽  
pp. 504-508
Author(s):  
D. Tr. Dochev ◽  
D. D. Bainov
Keyword(s):  
Differential Equations ◽  
Existence Of A Solution ◽  
Deviating Argument ◽  
Multivalued Differential Equations

scholarly journals Averaging of multivalued differential equations

2003 ◽  
Vol 2003 (25) ◽  
pp. 1615-1622 ◽  
Author(s):  
G. Grammel
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fast Subsystem ◽  
Slow Subsystem ◽  
Multivalued Differential Equations

Nonlinear multivalued differential equations with slow and fast subsystems are considered. Under transitivity conditions on the fast subsystem, the slow subsystem can be approximated by an averaged multivalued differential equation. The approximation in the Hausdorff sense is of orderO(ϵ1/3)asϵ→0.

Approximate controllability of non-instantaneous impulsive semilinear measure driven control system with infinite delay via fundamental solution

2020 ◽  
Author(s):  
Surendra Kumar ◽  
Syed Mohammad Abdal
Keyword(s):  
Fundamental Solution ◽  
Differential Equations ◽  
Control Systems ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Existence Of A Solution ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
New Class

Abstract This article investigates a new class of non-instantaneous impulsive measure driven control systems with infinite delay. The considered system covers a large class of the hybrid system without any restriction on their Zeno behavior. The concept of measure differential equations is more general as compared to the ordinary impulsive differential equations; consequently, the discussed results are more general than the existing ones. In particular, using the fundamental solution, Krasnoselskii’s fixed-point theorem and the theory of Lebesgue–Stieltjes integral, a new set of sufficient conditions is constructed that ensures the existence of a solution and the approximate controllability of the considered system. Lastly, an example is constructed to demonstrate the effectiveness of obtained results.

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