Nonexistence and existence results of an optimal control problem governed by a class of multisolution semilinear elliptic equations

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• 作者：Shu Luan ^{luans257@yeah.net" class="auth_mail" title="E-mail the corresponding author}
• 关键词：49J20 ; 35J61
• 刊名：Nonlinear Analysis
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：128
• 期：Complete
• 页码：380-390
• 全文大小：603 K

文摘

An optimal control problem governed by a class of multisolution semilinear elliptic equations is studied in this paper. It is pointed out that the control domain and cost functional are nonconvex. By analyzing the maximum condition for an optimal relaxed control, one nonexistence and some existence results of an optimal pair are obtained. The idea of using relaxed controls is mainly derived from the paper (Lou, 2007) by Lou where a linear and well-posed controlled system was considered. The present paper is mainly devoted to discussing the case not contained in Lou (2007).