Existence of multiple periodic solutions to asymptotically linear wave equations in a ball

doi:10.1007/s00526-017-1154-4

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	Existence of multiple periodic solutions to asymptotically linear wave equations in a ball
	Chen, Jianyi 1; Zhang, Zhitao2,3
	2017-06-01
发表期刊	CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
ISSN	0944-2669
卷号	56 期号:3 页码:25
摘要	This paper is concerned with the Dirichlet problem of the asymptotically linear wave equation u(tt) - Delta u = g(t, x, u) in a n-dimensional ball with radius R, where n > 1 and g(t, x, u) is radially symmetric in x and T-periodic in time. An interesting feature is that the solvable of the problem depends on the space dimension n and the arithmetical properties of R and T. Based on the spectral properties of the radially symmetric wave operator, we use the saddle point reduction and variational methods to construct at least three radially symmetric solutions with time period T, when T is a rational multiple of R and g(t, x, u) satisfies some monotonicity and asymptotically linear conditions.
关键词	Asymptotically linear wave equation Multi-dimensional problem Periodic solutions Variational method
DOI	10.1007/s00526-017-1154-4
语种	英语
资助项目	National Natural Science Foundation of China[11325107] ; National Natural Science Foundation of China[11271353] ; National Natural Science Foundation of China[11331010] ; Natural Science Foundation of Shandong Province[ZR2016AQ04] ; Research Foundation for Advanced Talents of Qingdao Agricultural University[6631114328] ; Science and Technology Program of Shandong Universities[J16LI04]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000402817100003
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25523
专题	数学所
通讯作者	Zhang, Zhitao
作者单位	1.Qingdao Agr Univ, Sci & Informat Coll, Qingdao 266109, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Chen, Jianyi,Zhang, Zhitao. Existence of multiple periodic solutions to asymptotically linear wave equations in a ball[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS,2017,56(3):25.
APA	Chen, Jianyi,&Zhang, Zhitao.(2017).Existence of multiple periodic solutions to asymptotically linear wave equations in a ball.CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS,56(3),25.
MLA	Chen, Jianyi,et al."Existence of multiple periodic solutions to asymptotically linear wave equations in a ball".CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS 56.3(2017):25.