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On the interior spike solutions for some singular perturbation problems

Published online by Cambridge University Press:  14 November 2011

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

For some singular perturbed Dirichlet and Neumann problems in a bounded smooth domain, we study solutions which have a spike in the interior. We obtain both necessary and sufficient conditions for the existence of interior spike solutions. We use, among others, the methods of projections and viscosity solutions, weak convergence of measures and Liapunov–Schmidt reduction.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 4 , 1998 , pp. 849 - 874
Copyright
Copyright © Royal Society of Edinburgh 1998

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