Many solutions for elliptic equations with critical exponents

doi:10.1007/s11856-008-0023-4

CSpace > 应用数学研究所

	Many solutions for elliptic equations with critical exponents
	Han, Pigong
	2008-03-01
发表期刊	ISRAEL JOURNAL OF MATHEMATICS
ISSN	0021-2172
卷号	164 期号:1 页码:125-152
摘要	Let Omega be an open bounded domain in R-N( N >= 3) and 2* = 2N/N-2. We are concerned with two kinds of critical elliptic problems. The first one is () -Delta u -mu u/vertical bar x vertical bar(2) = lambda u + vertical bar u vertical bar(m-2) u + theta vertical bar u vertical bar(2-2) u u is an element of H-0(1)(Omega), where 0 is an element of Omega, 0 < mu < (N-2/2)(2), 2 < m < 2* and lambda > 0. By using the fountain theorem and concentration estimates, if N >= 7 and theta > 0, we establish the existence of infinitely many solutions for the following regularization of () with small number is an element of > 0 -Delta u -mu u/vertical bar x vertical bar(2) + is an element of = lambda u + vertical bar u vertical bar(m-2) u + theta vertical bar u vertical bar(2-2) u u is an element of H-0(1)(Omega). Then if theta > 0 is suitably small, we obtain many solutions for problem () by taking the process of approximation. The second problem is -Delta u = vertical bar u vertical bar(2-2)u + t vertical bar u vertical bar(q-1)u u is an element of H-0(1)(Omega), where q is an element of (0,1) t > 0. By using similar methods as in (*), we prove that if N >= 7, 4/N-2 < q < 1 and t > 0, there exist infinitely many solutions with positive energy. In particular, we give a positive answer to one open problem proposed by Ambrosetti, Brezis and Cerami [1].
DOI	10.1007/s11856-008-0023-4
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000254774600006
出版者	HEBREW UNIV MAGNES PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/6905
专题	应用数学研究所
通讯作者	Han, Pigong
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, Pigong. Many solutions for elliptic equations with critical exponents[J]. ISRAEL JOURNAL OF MATHEMATICS,2008,164(1):125-152.
APA	Han, Pigong.(2008).Many solutions for elliptic equations with critical exponents.ISRAEL JOURNAL OF MATHEMATICS,164(1),125-152.
MLA	Han, Pigong."Many solutions for elliptic equations with critical exponents".ISRAEL JOURNAL OF MATHEMATICS 164.1(2008):125-152.