Approximate controllability of second order impulsive systems with state-dependent delay in Banach spaces. (English) Zbl 1483.34106
Summary: In this paper, we consider the second order semilinear impulsive differential equations with state-dependent delay. First, we consider a linear second order system and establish the approximate controllability result by using a feedback control. Then, we obtain sufficient conditions for the approximate controllability of the considered system in a separable, reflexive Banach space via properties of the resolvent operator and Schauder’s fixed point theorem. Finally, we apply our results to investigate the approximate controllability of the impulsive wave equation with state-dependent delay.
MSC:
| 34K30 | Functional-differential equations in abstract spaces |
| 34K43 | Functional-differential equations with state-dependent arguments |
| 34K45 | Functional-differential equations with impulses |
| 93B05 | Controllability |
Keywords:
impulsive functional differential equations; approximate controllability; Schauder’s fixed point theorem; cosine family; resolvent operatorReferences:
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