Existence and nonexistence of entire solutions for non-cooperative cubic elliptic systems

Hugo Tavares, Susanna Terracini, Gianmaria Verzini +1

In this paper we deal with the cubic Schrödinger system $-\Delta u_i={\sum }_{j=1}^n{\beta }_{ij}{u}_j^2{u}_i$, $u_1,\dots ,u_n\ge 0$ in ${\mathbb{R}}^N(N\le 3)$, where $\beta =({\beta }_{i,j}{)}_{ij}$ is a s…