Abstract
It is the purpose of this note to study the inhomogeneous coupled Schrodinger system
iu(j)+Delta u(j)+/-vertical bar x vertical bar(b) ((k=1)Sigma(m) a(jk)vertical bar u(k)vertical bar(p))vertical bar u(j) vertical bar p(-2) u(j) = 0.
Indeed, in the stationary case, the existence of ground states is proved and a sharp inhomogeneous Gagliardo-Nirenberg-type inequality is established. In the evolving case, the existence of global/non-global focusing solutions is investigated using the potential well method. Finally, the decay of defocusing global solutions is studied.