We study the stationary Swift--Hohenberg equation (Δ + 1)² u - α u - β u² + u³=0 in the whole space Rⁿ, 2≤ n ≤ 7. We develop and modify the variational approach introduced by Lerman, Naryshkin and Nazarov (2020) and obtain a series of periodic solutions with certain additional symmetries.
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Kolonitskii et al. (2024) studied this question.
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