Abstract
In this short paper, we consider solutions u ∈ C2(ℝN, ℝM) (with N,M ≥ 1) of the Ginzburg–Landau system Δu = u(|u|2 - 1). For N = 3 and M = 2, we prove that every solution satisfying ∫ℝ3 (|u|2 - 1)2 < +∞, is constant and of unit norm. We also give necessary and sufficient conditions, on the integers N and M, ensuring a Liouville property for finite potential energy solutions of the system under consideration.
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