The existence, uniqueness and nonexistence of the ground state to the N-coupled Schrödinger systems in.

Consider the following Schrödinger system: where either or is a smooth bounded domain. Note that the cubic nonlinearities and the coupling terms are of critical growth whenever dimension . We give a characterization of the least energy solutions when or is a smooth bounded domain of , if the coupling matrix is positively or negatively definite with and exists and satisfies for . Furthermore, when and , we obtain a nonexistence theorem about the least energy solutions provided attraction and repulsion coexist, i.e. some of are positive but some others are negative. [ABSTRACT FROM AUTHOR]