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Periodic solutions for the Allen-Cahn equation

Rui Huang, Haochuan Huang, Shanming Ji and Jingxue Yin
Advances in Difference Equations 2015 (1) (2015)
DOI: 10.1186/s13662-015-0631-3
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Bump solutions for the mesoscopic Allen–Cahn equation in periodic media

Matteo Novaga and Enrico Valdinoci
Calculus of Variations and Partial Differential Equations 40 (1-2) 37 (2011)
DOI: 10.1007/s00526-010-0332-4
See this article