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

S. B. Kolonitskii, L. M. Lerman, A. I. Nazarov

We study the stationary Swift--Hohenberg equation $(\Delta +1{)}^{2}u-\alpha u-\beta u^2+u^3=0$ in the whole space ${\mathbb{R}}^n$, $2\le n\le 7$. We develop and modify the variational approach…