[hal-01076363] Qualitative properties of a nonlinear system involving the p-Laplacian operator and a DeGiorgi type result

In this article we consider the nonlinear system involving the p-Laplacian    u p−2 u = u p−1 v p v p−2 v = v p−1 u p on R u ≥ 0 v ≥ 0 for which we prove symmetry asymptotic behavior and non degeneracy properties Next we prove a De Giorgi Type result in dimension 2 under some additional growth and monotonicity assumptions Mathematics Subject Classification 35 J20 35 J 50



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