Existence of positive solutions for a general nonlinear eigenvalue problem

doi:10.1007/s10255-011-0076-8

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	Existence of positive solutions for a general nonlinear eigenvalue problem
	Cheng, Xi-you 1,2; Zhang, Zhi-tao1
	2011-07-01
发表期刊	ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
ISSN	0168-9673
卷号	27 期号:3 页码:367-372
摘要	Let Omega subset of (R)n be a bounded domain, H = L(2)(Omega), L : D( L) subset of H -> H be an unbounded linear operator, f is an element of C((Omega) over bar x R, R) and lambda is an element of R. The paper is concerned with the existence of positive solutions for the following nonlinear eigenvalue problem Lu = lambda f( x, u), u is an element of D(L), which is the general form of nonlinear eigenvalue problems for differential equations. We obtain the global structure of positive solutions, then we apply the results to some nonlinear eigenvalue problems for a second-order ordinary differential equation and a fourth-order beam equation, respectively. The discussion is based on the fixed point index theory in cones.
关键词	unbounded linear operator fixed point index positive solution
DOI	10.1007/s10255-011-0076-8
语种	英语
资助项目	National Natural Science Foundation of Jiangsu Province[10KJB110004] ; National Natural Science Foundation of Jiangsu Province[08KJD110010]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000291599500003
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/12888
专题	数学所
通讯作者	Cheng, Xi-you
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China 2.Nanjing Audit Univ, Dept Appl Math, Nanjing 210029, Peoples R China
推荐引用方式 GB/T 7714	Cheng, Xi-you,Zhang, Zhi-tao. Existence of positive solutions for a general nonlinear eigenvalue problem[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,2011,27(3):367-372.
APA	Cheng, Xi-you,&Zhang, Zhi-tao.(2011).Existence of positive solutions for a general nonlinear eigenvalue problem.ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,27(3),367-372.
MLA	Cheng, Xi-you,et al."Existence of positive solutions for a general nonlinear eigenvalue problem".ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES 27.3(2011):367-372.