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Optimal control of second order stochastic evolution hemivariational inequalities with Poisson jumps. (English) Zbl 1391.49017

Summary: The purpose of this article is to study the optimal control problem of second order stochastic evolution hemivariational inequalities with Poisson jumps by virtue of cosine operator theory in the Hilbert space. Initially, the sufficient conditions for existence of mild solution of the proposed system are verified by applying properties of Clarke’s subdifferential operator and fixed point theorem in multivalued maps. Further, we formulated and proved the existence results for optimal control of the proposed system with corresponding cost function by using Balder theorem. Finally an example is provided to illustrate the main results.

MSC:

49J40 Variational inequalities
49J55 Existence of optimal solutions to problems involving randomness
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
93E20 Optimal stochastic control
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