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http://bura.brunel.ac.uk/handle/2438/517
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. |
URI: | http://bura.brunel.ac.uk/handle/2438/517 |
Appears in Collections: | Dept of Mathematics Research Papers Mathematical Sciences |
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9-mult9.pdf | 230.33 kB | Adobe PDF | View/Open |
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