Infinitely many small solutions for the Kirchhoff equation with local sublinear nonlinearities

doi:10.1016/j.jmaa.2015.10.075

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	Infinitely many small solutions for the Kirchhoff equation with local sublinear nonlinearities
	Li, Lin 1; Zhong, Xin 2
	2016-03-01
发表期刊	JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN	0022-247X
卷号	435 期号:1 页码:955-967
摘要	We study the following nonlinear Kirchhoff equation on the whole space - (1 + b integral(R3) (vertical bar del u vertical bar(2) + V(x)u(2)) dx) [Delta u + V(x)u] = f(x, u) in R-3, where b > 0 is a constant and the nonlinear term f(x, u) is only locally defined for vertical bar u vertical bar small and satisfies some mild conditions. It is proved that the above problem admits infinity many weak solutions provided that some additional assumptions are satisfied. Moreover, we show that these solutions tend to zero in L-infinity(R-3). Our method relies upon a variant of the symmetric mountain pass lemma due to Kajikiya and Moser iteration method. (C) 2015 Elsevier Inc. All rights reserved.
关键词	Kirchhoff equation Variational methods Local sublinear nonlinearities Symmetric mountain pass lemma
DOI	10.1016/j.jmaa.2015.10.075
语种	英语
资助项目	Chongqing Technology and Business University[2015-56-09]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000365928200058
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/21468
专题	中国科学院数学与系统科学研究院
通讯作者	Li, Lin
作者单位	1.Chongqing Technol & Business Univ, Sch Math & Stat, Chongqing 400067, Peoples R China 2.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Li, Lin,Zhong, Xin. Infinitely many small solutions for the Kirchhoff equation with local sublinear nonlinearities[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,2016,435(1):955-967.
APA	Li, Lin,&Zhong, Xin.(2016).Infinitely many small solutions for the Kirchhoff equation with local sublinear nonlinearities.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,435(1),955-967.
MLA	Li, Lin,et al."Infinitely many small solutions for the Kirchhoff equation with local sublinear nonlinearities".JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 435.1(2016):955-967.