S. B. Kolonitskii

Entire solutions to the Swift--Hohenberg equation via variational approach

We study the stationary Swift--Hohenberg equation $(Δ+ 1)^2 u - αu - βu^2 + u^3=0$ in the whole space $\mathbb R^n$, $2\le n \le 7$. 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.