Interaction between the geometry of the boundary and positive solutions of a semilinear neumann problem with critical nonlinearity

AdimurthiPacella, F. ; Yadava, S. L. (1993) Interaction between the geometry of the boundary and positive solutions of a semilinear neumann problem with critical nonlinearity Journal of Functional Analysis, 113 (2). pp. 318-350. ISSN 0022-1236

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1006/jfan.1993.1053

Abstract

We consider the problem: -Δu + λu = un + 2)(n - 2, u > 0 in Ω , ∂u/∂v = 0 on ∂Ω, where Ω is a bounded smooth domain in Rn (n ≥ 3). We show that, for λ large, least-energy solutions of the above problem have a unique maximum point Pλ on ∂Ω and the limit points of Pλ, as λ → ∞ are contained in the set of the points of maximum mean curvature. We also prove that, if ∂Ω has k peaks then the equation has at least k solutions for λ large.

Item Type:Article
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ID Code:60644
Deposited On:09 Sep 2011 09:03
Last Modified:09 Sep 2011 09:03

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