Jm. Mercier, EXISTENCE OF FINITE-ENERGY SOLUTIONS FOR SEMILINEAR ELLIPTIC-SYSTEMS, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 323(11), 1996, pp. 1169-1174
We show that the only solution of R (epsilon(1), epsilon(2)) which are
semi-linear elliptic systems treated in the full space R(3) for real
valued (u, v) functions, is the trivial one. However, we show that the
R(-1, -1) system admits solutions that are non trivial finite energy
perturbations of the particular (a, 0) solution, with a not equal 0.