Existence of clustering high dimensional bump solutions of superlinear elliptic problems on expanding annuli
- Title
- Existence of clustering high dimensional bump solutions of superlinear elliptic problems on expanding annuli
- Author
- 김승혁
- Keywords
- Concentration phenomena; Expanding annuli; Supercritical problem
- Issue Date
- 2013-11
- Publisher
- Elsevier Science
- Citation
- Journal of Functional Analysis, 2013, 265(9), P.955-1980
- 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. (C) 2013 Elsevier Inc. All rights reserved.
- URI
- https://www.sciencedirect.com/science/article/pii/S002212361300267X?via%3Dihubhttp://hdl.handle.net/20.500.11754/51327
- ISSN
- 0022-1236; 1096-0783
- DOI
- 10.1016/j.jfa.2013.07.008
- Appears in Collections:
- COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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