Uniqueness and stability of the saddle-shaped solution to the fractional Allen-Cahn equation

Juan-Carlos Felipe-Navarro, Tomás Sanz-Perela

In this paper we prove the uniqueness of the saddle-shaped solution to the semilinear nonlocal elliptic equation $(-\Delta {)}^{\gamma }u=f(u)$ in ${\mathbb{R}}^{2m}$, where $\gamma \in (0,1)$ and $f$ is…