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Solutions with boundary layer and positive peak for an elliptic Dirichlet problem

Published online by Cambridge University Press:  12 July 2007

Gongbao Li ,
Jianfu Yang  and
Shusen Yan
Gongbao Li
Affiliation:
Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, PO Box 71010, Wuhan 430071, People's Republic of China
Jianfu Yang
Affiliation:
Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, PO Box 71010, Wuhan 430071, People's Republic of China
Shusen Yan
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia
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Abstract

In this paper, we study existence of solutions with boundary layer and peaks for an elliptic problem. We prove that the problem has a mountain-pass-type solution, which has a boundary layer and a single peak near the boundary. Moreover, we also study the existence of solutions with interior peak.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 3 , June 2004 , pp. 515 - 536
Copyright
Copyright © Royal Society of Edinburgh 2004

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