Multiple positive solutions of nonhomogeneous elliptic systems involving critical Sobolev exponents

doi:10.1016/j.na.2005.04.053

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	Multiple positive solutions of nonhomogeneous elliptic systems involving critical Sobolev exponents
	Han, PG
	2006-02-15
发表期刊	NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
ISSN	0362-546X
卷号	64 期号:4 页码:869-886
摘要	In this paper, we study the existence of multiple positive solutions to the following elliptic system: -Delta u=[2 alpha/(alpha+beta)]u vertical bar u vertical bar(alpha-2)vertical bar v vertical bar(beta)+epsilon f(x), -Delta v=[2 beta/(alpha+beta)]vertical bar u vertical bar(alpha) v vertical bar v vertical bar(beta-2)+epsilon g(x) in Omega;u,v > 0 in Omega; and u=v=0 on partial derivative Omega (), where Omega is abounded domain in R-N(N >= 3); f, g is an element of C-1(Omega);and alpha, beta > 1. For the subcritical and critical cases, we prove that problem () has at least two solutions for any epsilon is an element of (0, epsilon(0)) and has no solution for any epsilon > epsilon, epsilon(0) <= epsilon. In the supercritical case, we find that the existence of solutions to problem (*) is closely related to the existence of nonnegative solutions for two linear elliptic problems. (c) 2005 Elsevier Ltd. All rights reserved.
关键词	elliptic system sub-supersolution method variational approach (PS)(c) sequence critical point
DOI	10.1016/j.na.2005.04.053
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000234957900014
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/3735
专题	应用数学研究所
通讯作者	Han, PG
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Han, PG. Multiple positive solutions of nonhomogeneous elliptic systems involving critical Sobolev exponents[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,2006,64(4):869-886.
APA	Han, PG.(2006).Multiple positive solutions of nonhomogeneous elliptic systems involving critical Sobolev exponents.NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,64(4),869-886.
MLA	Han, PG."Multiple positive solutions of nonhomogeneous elliptic systems involving critical Sobolev exponents".NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 64.4(2006):869-886.