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.

Existence of clustering high dimensional bump solutions of superlinear elliptic problems on expanding annuli / Jaeyoung, Byeon; Seunghyeok, Kim; Pistoia, Angela. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 265:9(2013), pp. 1955-1980. [10.1016/j.jfa.2013.07.008]

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

PISTOIA, Angela
2013

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.
2013
concentration phenomena; expanding annuli; supercritical problem
01 Pubblicazione su rivista::01a Articolo in rivista
Existence of clustering high dimensional bump solutions of superlinear elliptic problems on expanding annuli / Jaeyoung, Byeon; Seunghyeok, Kim; Pistoia, Angela. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 265:9(2013), pp. 1955-1980. [10.1016/j.jfa.2013.07.008]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/781650
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