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Nonexistence and Existence of an Optimal Control Problem Governed by a Class of Semilinear Elliptic Equations

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Abstract

An optimal control problem governed by a class of semilinear elliptic equations is considered in this paper. Using relaxed controls, the nonexistence and existence results of an optimal control are obtained.

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Acknowledgements

The author would like to thank Professor Lou Hongwei for his helpful suggestions.

This work was partially supported by the National Natural Science Foundation of China under grants 11226246 and 10901032 and the Foundation for Distinguished Young Talents in Higher Education of Guangdong under grant 2012LYM_0090.

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Authors and Affiliations

  1. School of Mathematics and Computation, Zhanjiang Normal College, Zhanjiang, Guangdong, 524048, China

    Shu Luan

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  1. Shu Luan
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Correspondence to Shu Luan.

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Communicated by Aram Arutyunov.

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Luan, S. Nonexistence and Existence of an Optimal Control Problem Governed by a Class of Semilinear Elliptic Equations. J Optim Theory Appl 158, 1–10 (2013). https://doi.org/10.1007/s10957-012-0244-x

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  • DOI: https://doi.org/10.1007/s10957-012-0244-x

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