We consider the system ∆u−Wu(u) = 0, for u : R → R, W : R → R, where Wu(u) = ( Wu1(u),Wu2(u) ) , in an equivariant class of functions. We prove that there exists u, a two-dimensional solution, which satisfies the conditions u(x1, x2)→ a±, as x1 → ±∞, where a, a− ∈ R are the two global minima of the potential W . We also consider the problem on bounded… (More)

@inproceedings{Alikakos2008OnAE,
title={On an elliptic system with symmetric potential possessing two global minima},
author={Nicholas D. Alikakos and Giorgio Fusco},
year={2008}
}