Qualitative properties of saddle-shaped solutions to bistable diffusion equations

Xavier Cabre, Joana Terra

We consider the elliptic equation $-\Delta u=f(u)$ in the whole ${\mathbb{R}}^{2m}$, where $f$ is of bistable type. It is known that there exists a saddle-shaped solution in ${\mathbb{R}}^{2m}$. This is a…