was supported by National Natural Science Foundation of China(Grant Nos.11271265 and 11331010);Beijing Center for Mathematics and Information Interdisciplinary Sciences
In the case where either the potentials Vj,μj andβare periodic or Vj are well-shaped andμj andβare anti-well-shaped,existence of a positive ground state of the Schrdinger system -Δu1+V1(x)u1=μ1(x)u31+β(x)u1u22i...