Existence of clustering high dimensional bump solutions of superlinear elliptic problems on expanding annuli

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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. (C) 2013 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2013-11
Language
English
Article Type
Article
Citation

JOURNAL OF FUNCTIONAL ANALYSIS, v.265, no.9, pp.1955 - 1980

ISSN
0022-1236
DOI
10.1016/j.jfa.2013.07.008
URI
http://hdl.handle.net/10203/254437
Appears in Collection
MA-Journal Papers(저널논문)
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