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.
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