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December, 2017 Optimal Control of Second Order Stochastic Evolution Hemivariational Inequalities with Poisson Jumps
Palanisamy Muthukumar, Nagarajan Durga, Fathalla A. Rihan, Chinnathambi Rajivganthi
Taiwanese J. Math. 21(6): 1455-1475 (December, 2017). DOI: 10.11650/tjm/8001

Abstract

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.

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Palanisamy Muthukumar. Nagarajan Durga. Fathalla A. Rihan. Chinnathambi Rajivganthi. "Optimal Control of Second Order Stochastic Evolution Hemivariational Inequalities with Poisson Jumps." Taiwanese J. Math. 21 (6) 1455 - 1475, December, 2017. https://doi.org/10.11650/tjm/8001

Information

Received: 9 June 2016; Revised: 30 December 2016; Accepted: 14 February 2017; Published: December, 2017
First available in Project Euclid: 17 August 2017

zbMATH: 06871377
MathSciNet: MR3732914
Digital Object Identifier: 10.11650/tjm/8001

Subjects:
Primary: 47J20 , 49J15 , 60G57 , 65C30

Keywords: Clarke's subdifferential , Hemivariational inequalities , optimal control , Poisson jumps , stochastic evolution equations

Rights: Copyright © 2017 The Mathematical Society of the Republic of China

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Vol.21 • No. 6 • December, 2017
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