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 = u^{n + 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 P_{λ} on ∂Ω and the limit points of P_{λ}, 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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Source: | Copyright of this article belongs to Elsevier Science. |

ID Code: | 60644 |

Deposited On: | 09 Sep 2011 09:03 |

Last Modified: | 09 Sep 2011 09:03 |

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