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Title: Multi-Peak Solutions for a Wide Class of Singular Perturbation Problems
Authors: Winter, M
Wei, J
Keywords: Nonlinear Elliptic Equations;Phase Transition
Issue Date: 1999
Publisher: Cambridge University Press
Citation: J London Math Soc 59 (1999), 585-606
Abstract: In this paper we are concerned with a wide class of singular perturbation problems arising from such diverse fields as phase transitions, chemotaxis, pattern formation, population dynamics and chemical reaction theory. We study the corresponding elliptic equations in a bounded domain without any symmetry assumptions. We assume that the mean curvature of the boundary has \overline{M} isolated, non-degenerate critical points. Then we show that for any positive integer m\leq \overline{M} there exists a stationary solution with M local peaks which are attained on the boundary and which lie close to these critical points. Our method is based on Liapunov-Schmidt reduction.
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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