Fractional Schr枚dinger equations with potential and optimal controls

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• 作者：JinRong Wang^a ; ^{wjr9668@126.com} ; Yong Zhou^b ; ^{yzhou@xtu.edu.cn} ; Wei Wei^a ; ^{wwei@gzu.edu.cn}
• 关键词：Fractional Schr&ouml ; dinger equations ; Potential ; Mild solutions ; Existence ; Local stability and attractivity ; Optimal controls
• 刊名：Nonlinear Analysis ; Real World Applications
• 出版年：2012
• 期刊代码：44_14681218
• 类别：mt
• 出版时间：December, 2012
• 卷：13
• 期：6
• 页码：2755-2766
• 文件大小：281 K

摘要

In this paper, we study fractional Schr枚dinger equations with potential and optimal controls. The first novelty is a suitable concept on a mild solution for our problems. Existence, uniqueness, local stability and attractivity, and data continuous dependence of mild solutions are also presented respectively. The second novelty is an initial study on the optimal control problems for the controlled fractional Schr枚dinger equations with potential. Existence and uniqueness of optimal pairs for the standard Lagrange problem are obtained.