On an elliptic system with symmetric potential possessing two global minima

Abstract

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)

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Cite this paper

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