Multiplicity of layered solutions for Allen-Cahn systems with symmetric double well potential

Francesca G. Alessio, Piero Montecchiari

We study the existence of solutions $u:{\mathbb{R}}^3\to {\mathbb{R}}^2$ for the semilinear elliptic systems \begin{equation}\label{eq:abs} -Δu(x,y,z)+\nabla W(u(x,y,z))=0, \end{equation} where $W:…