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

被引：1

作者：

Luan, Shu ^{[1
]}

机构：

[1] Lingnan Normal Univ, Sch Math & Computat Sci, Zhanjiang 524048, Guangdong, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2015年 / 128卷

基金：

中国国家自然科学基金;

关键词：

Optimal control; Semilinear elliptic equation; Multisolution; Nonexistence; Existence; Relaxed control; CONVEXITY; SYSTEMS;

D O I：

10.1016/j.na.2015.08.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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). (c) 2015 Elsevier Ltd. All rights reserved.

引用

页码：380 / 390

页数：11

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