Existence and approximate controllability of semilinear measure driven systems with nonlocal conditions. (English) Zbl 1493.93006
In this paper the authors have studied the existence of mild solutions and approximate controllability for measure driven evolution system with nonlocal conditions. First,they obtained the existence of mild solutions and approximate controllability for the concerned problem by constructing new Green’s function and control function involving Gramian controllability operator. The results are established by using the Schauder fixed point theorem and semigroup theory. Finally, two examples are given to illustrate the theoretical results.
Reviewer: Krishnan Balachandran (Coimbatore)
MSC:
| 93B05 | Controllability |
| 26A42 | Integrals of Riemann, Stieltjes and Lebesgue type |
| 34A38 | Hybrid systems of ordinary differential equations |
| 34K30 | Functional-differential equations in abstract spaces |
| 34K35 | Control problems for functional-differential equations |
Keywords:
approximate controllability; \(C_0\)-semigroup; Lebesgue-Stieltjes integral; measure driven evolution equationReferences:
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