On Littlewood's boundedness problem for relativistic oscillators with singular potentials

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• 作者：Yu Han ^{yhan@mail.bnu.edu.cn} ; Xiong Li ; ^{xli@bnu.edu.cn}
• 关键词：Relativistic oscillators ; Singular potentials ; Boundedness ; Quasi-periodic solutions ; Moser's twist theorem
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 May 2017
• 年：2017
• 卷：449
• 期：2
• 页码：1424-1471
• 全文大小：583 K
• 卷排序：449

文摘

In this paper, we study the following nonlinear differential equations of motions of relativistic oscillators with singular potentialsddt(x′1−(x′)2)+V′(x)=p(t), where V is a singular potential and p is a 1-periodic function. We will prove the boundedness of all solutions and the existence of infinitely many quasi-periodic solutions via Moser's twist theorem.