Existence of clustering high dimensional bump solutions of superlinear elliptic problems on expanding annuliopen access
- Authors
- Byeon, Jaeyoung; Kim, Seunghyeok; Pistoia, Angela
- Issue Date
- Nov-2013
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Concentration phenomena; Expanding annuli; Supercritical problem
- Citation
- JOURNAL OF FUNCTIONAL ANALYSIS, v.265, pp.1955 - 1980
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF FUNCTIONAL ANALYSIS
- Volume
- 265
- Start Page
- 1955
- End Page
- 1980
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/161437
- DOI
- 10.1016/j.jfa.2013.07.008
- ISSN
- 0022-1236
- Abstract
- We consider the nonlinear elliptic problem-Delta u = u(p) in Omega(R), u > 0 in Omega(R), u = 0 in Omega(R)where p > 1 and Omega(R) = {x is an element of R-N: R < vertical bar x vertical bar < R + 1} with N >= 3. It is known that as R -> infinity, the number of nonequivalent solutions of the above problem goes to infinity when p is an element of (N + 2)/(N - 2)), N >= 3. Here we prove the same phenomenon for any p > 1 by finding O (N - 1)-symmetric clustering bump solutions which concentrate near the set {(x(1), ... , x(N)) is an element of Omega(R): x(N) = 0} for large R > 0.
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Collections - 서울 자연과학대학 > 서울 수학과 > 1. Journal Articles
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