Solutions of a system of diffusion equations

doi:10.1007/s11784-007-0023-8

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	Solutions of a system of diffusion equations
	Ding, Yanheng1 ; Luan, Shixia 2; Willem, Michel 3
	2007-09-01
发表期刊	JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
ISSN	1661-7738
卷号	2 期号:1 页码:117-139
摘要	We study existence and multiplicity of homoclinic type solutions to the following system of diffusion equations on R x Omega: {partial derivative(t)u - Delta(x)u + b(t, x) . del(x) u + V(x)u = H-v (t, x, u, v), {-partial derivative(t)v - Delta(x)v - b(t, x) . del(x) v + V(x)v = H-u (t, x, u, v), where Omega = R-N or Omega is a smooth bounded domain of R-N, z = (u, v) : R x Omega -> R-m x R-m, and b is an element of C-1 (R x (Omega) over bar, R-N), V is an element of C((Omega) over bar, R), H is an element of C-1 (R x (Omega) over bar x R-2m, R), all three depending periodically on t and x. We assume that H(t, x, 0) 0 and H is asymptotically quadratic or superquadratic as vertical bar z vertical bar -> infinity. The superquadratic condition is more general than the usual one. By establishing a proper variational setting based on some recent critical point theorems we obtain at least one nontrivial solution, and also infinitely many solutions provided H is moreover symmetric in z.
关键词	Spectrum infinitely many homoclinics asymptotically linear superlinear critical points
DOI	10.1007/s11784-007-0023-8
语种	英语
资助项目	NSFC[10640420049]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000205771800007
出版者	SPRINGER BASEL AG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/4569
专题	数学所
通讯作者	Ding, Yanheng
作者单位	1.Chinese Acad Sci, Inst Math, AMSS, Beijing 100080, Peoples R China 2.Qufu Normal Univ, Dept Math, Shandong 273165, Peoples R China 3.Catholic Univ Louvain, Dept Math Pures & Appl, B-1348 Louvain, Belgium
推荐引用方式 GB/T 7714	Ding, Yanheng,Luan, Shixia,Willem, Michel. Solutions of a system of diffusion equations[J]. JOURNAL OF FIXED POINT THEORY AND APPLICATIONS,2007,2(1):117-139.
APA	Ding, Yanheng,Luan, Shixia,&Willem, Michel.(2007).Solutions of a system of diffusion equations.JOURNAL OF FIXED POINT THEORY AND APPLICATIONS,2(1),117-139.
MLA	Ding, Yanheng,et al."Solutions of a system of diffusion equations".JOURNAL OF FIXED POINT THEORY AND APPLICATIONS 2.1(2007):117-139.