Deformation theorems on non-metrizable vector spaces and applications to critical point theory

doi:10.1002/mana.200410420

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	Deformation theorems on non-metrizable vector spaces and applications to critical point theory
	Bartsch, Thomas ; Ding, Yanheng
	2006
发表期刊	MATHEMATISCHE NACHRICHTEN
ISSN	0025-584X
卷号	279 期号:12 页码:1267-1288
摘要	Let E be a Banach space and Phi : E -> R a C-1-functional. Let P be a family of semi-norms on E which separates points and generates a (possibly non-metrizable) topology T-p on E weaker than the norm topology. This is a special case of a gage space, that is, a topological space where the topology is generated by a family of semi-metrics. We develop some critical point theory for Phi : (E, P) -> R. In particular, we prove deformation lemmas where the deformations are continuous with respect to T-p. In applications this yields a gain in compactness when Phi does not satisfy the Palais-Smale condition because one can work with the weak topology. We also prove some foundational results on gage spaces. In particular, we introduce the concept of Lipschitz continuity in this setting and prove the existence of Lipschitz continuous partitions of unity. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
关键词	critical point theory strongly indefinite functionals gage spaces
DOI	10.1002/mana.200410420
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000240364800001
出版者	WILEY-V C H VERLAG GMBH
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/2669
专题	数学所
通讯作者	Bartsch, Thomas
作者单位	1.Univ Giessen, Math Inst, D-35392 Giessen, Germany 2.Chinese Acad Sci, Inst Math, AMSS, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Bartsch, Thomas,Ding, Yanheng. Deformation theorems on non-metrizable vector spaces and applications to critical point theory[J]. MATHEMATISCHE NACHRICHTEN,2006,279(12):1267-1288.
APA	Bartsch, Thomas,&Ding, Yanheng.(2006).Deformation theorems on non-metrizable vector spaces and applications to critical point theory.MATHEMATISCHE NACHRICHTEN,279(12),1267-1288.
MLA	Bartsch, Thomas,et al."Deformation theorems on non-metrizable vector spaces and applications to critical point theory".MATHEMATISCHE NACHRICHTEN 279.12(2006):1267-1288.