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Homoclinic Solutions for Swift–Hohenberg and Suspension Bridge Type Equations

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Abstract:

We establish the existence of homoclinic solutions for a class of fourth-order equations which includes the Swift–Hohenberg model and the suspension bridge equation. In the first case, the nonlinearity has three zeros, corresponding to a double-well potential, while in the second case the nonlinearity is asymptotically constant on one side. The Swift–Hohenberg model is a higher-order extension of the classical Fisher–Kolmogorov model. Its more complicated dynamics give rise to further possibilities of pattern formation. The suspension bridge equation was studied by Chen and McKenna (J. Differential Equations 136 (1997), 325–355); we give a positive answer to an open question raised by the authors. © 2002 Elsevier Science (USA).

Document Type: Research Article

Affiliations: 1: Département de Mathématiques, Université Catholique de Louvain, 2 Chemin du Cyclotron, Louvain-la-Neuve, 1348, Belgium 2: School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, United Kingdom

Publication date: September 1, 2002

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