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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:449

Article

Han, Yu¹  Li, Xiong¹ 

[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

关键词: Relativistic oscillators;    Singular potentials;    Boundedness;    Quasi-periodic solutions;    Moser's twist theorem;   

DOI  :  10.1016/j.jmaa.2016.12.081

来源: Elsevier

【 摘 要 】

In this paper, we study the following nonlinear differential equations of motions of relativistic oscillators with singular potentials d/dt (x'/root 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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free