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Uniqueness and critical spectrum of boundary spike solutions

Published online by Cambridge University Press:  12 July 2007

Juncheng Wei
Juncheng Wei
Affiliation:
Juncheng Wei Department of Mathematics, Chinese University of Hong Kong, Shatin, Hong Kong (wei@math.cuhk.edu.hk)
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Abstract

We study the properties of single boundary spike solutions for the following singularly perturbed problem It is known that at a non-degenerate critical point of the mean curvature function H(P), there exists a single boundary spike solution. In this paper, we show that the single boundary spike solution is unique and moreover it has exactly (N − 1) small eigenvalues. We obtain the exact asymptotics of the small eigenvalues in terms of H(P).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 6 , December 2001 , pp. 1457 - 1480
Copyright
Copyright © Royal Society of Edinburgh 2001

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