Periodic Solutions to Klein-Gordon Systems with Linear Couplings

doi:10.1515/ans-2021-2138

	Periodic Solutions to Klein-Gordon Systems with Linear Couplings
	Chen, Jianyi 4; Zhang, Zhitao 1,2,3; Chang, Guijuan 4; Zhao, Jing 4
刊名	ADVANCED NONLINEAR STUDIES
	2021-08-01
卷号	21 期号:3 页码:633-660
关键词	Wave Equation Variational Method Klein-Gordon System Periodic Solutions
ISSN号	1536-1365
DOI	10.1515/ans-2021-2138
英文摘要	In this paper, we study the nonlinear Klein-Gordon systems arising from relativistic physics and quantum field theories {u(tt) - u(xx) + bu + epsilon v +f(t, x, u) = 0, v(tt) - v(xx) + bv + epsilon u + g(t, x, v) = 0, where u, v satisfy the Dirichlet boundary conditions on spatial interval [0, pi], b > 0 and f, g are 2 pi-periodic in t. We are concerned with the existence, regularity and asymptotic behavior of time-periodic solutions to the linearly coupled problem as e goes to 0. Firstly, under some superlinear growth and monotonicity assumptions on f and g, we obtain the solutions (u(epsilon), v epsilon) with time period 2 pi for the problem as the linear coupling constant e is sufficiently small, by constructing critical points of an indefinite functional via variational methods. Secondly, we give a precise characterization for the asymptotic behavior of these solutions, and show that, as epsilon -> 0, (u(epsilon), v(epsilon)) converge to the solutions of the wave equations without the coupling terms. Finally, by careful analysis which is quite different from the elliptic regularity theory, we obtain some interesting results concerning the higher regularity of the periodic solutions.
资助项目	National Natural Science Foundation of China[11701310] ; National Natural Science Foundation of China[11771428] ; National Natural Science Foundation of China[12031015] ; National Natural Science Foundation of China[12026217] ; Natural Science Foundation of Shandong Province[ZR2016AQ04] ; Research Foundation for Advanced Talents of Qingdao Agricultural University[6631114328]
WOS研究方向	Mathematics
语种	英语
出版者	WALTER DE GRUYTER GMBH
WOS记录号	WOS:000682145500007
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59020]
专题	中国科学院数学与系统科学研究院
通讯作者	Chen, Jianyi
作者单位	1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, HLM, Beijing 100049, Peoples R China 3.Jiangsu Univ, Sch Math Sci, Zhenjiang 212013, Jiangsu, Peoples R China 4.Qingdao Agr Univ, Sci & Informat Coll, Qingdao 266109, Peoples R China
推荐引用方式 GB/T 7714	Chen, Jianyi,Zhang, Zhitao,Chang, Guijuan,et al. Periodic Solutions to Klein-Gordon Systems with Linear Couplings[J]. ADVANCED NONLINEAR STUDIES,2021,21(3):633-660.
APA	Chen, Jianyi,Zhang, Zhitao,Chang, Guijuan,&Zhao, Jing.(2021).Periodic Solutions to Klein-Gordon Systems with Linear Couplings.ADVANCED NONLINEAR STUDIES,21(3),633-660.
MLA	Chen, Jianyi,et al."Periodic Solutions to Klein-Gordon Systems with Linear Couplings".ADVANCED NONLINEAR STUDIES 21.3(2021):633-660.