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MULTI-PEAK SOLUTIONS FOR A WIDE CLASS OF SINGULAR PERTURBATION PROBLEMS

Published online by Cambridge University Press:  01 April 1999

JUNCHENG WEI  and
MATTHIAS WINTER
JUNCHENG WEI
Affiliation:
Department of Mathematics, Chinese University of Hong Kong, Shatin, Hong Kong
MATTHIAS WINTER
Affiliation:
Mathematisches Institut A, Universität Stuttgart, D-70511 Stuttgart, Germany
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Abstract

This paper concerns a wide class of singular perturbation problems arising from such diverse fields as phase transitions, chemotaxis, pattern formation, population dynamics and chemical reaction theory. The corresponding elliptic equations in a bounded domain without any symmetry assumptions are studied. It is assumed that the mean curvature of the boundary has M isolated, non-degenerate critical points. Then it is shown that for any positive integer M[les ]M there exists a stationary solution with M local peaks which are attained on the boundary and which lie close to these critical points. The method is based on Lyapunov–Schmidt reduction.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 59 , Issue 2 , April 1999 , pp. 585 - 606
Copyright
The London Mathematical Society 1999

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