Arbitrary many boundary peak solutions for an elliptic Neumann problem with critical growth

Title
Arbitrary many boundary peak solutions for an elliptic Neumann problem with critical growth
Publication Date
2007
Author(s)
Wei, Juncheng
Yan, Shusen
Type of document
Journal Article
Language
en
Entity Type
Publication
Publisher
Elsevier Masson
Place of publication
France
DOI
10.1016/j.matpur.2007.07.001
UNE publication id
une:5761
Abstract
We consider the following problem, [**EQUATION**] where μ > 0 is a large parameter, Ω is a bounded domain in ℝⁿ, N ≤ 3 and 2* = 2N/(N - 2). Let H(P) be the mean curvature function of the boundary. Assuming that H(P) has a local minimum point with positive minimum, then for any integer k, the above problem has a k-boundary peaks solution. As a consequence, we show that if Ω is 'strictly convex', then the above problem has arbitrarily many solutions, provided that μ is large.
Link
link
Citation
Journal de Mathematiques Pures et Appliquees, 88(4), p. 350-378
ISSN
1776-3371
0021-7824
Start page
350
End page
378

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