“…When V 1 = V 2 and u = v, (1.1) becomes the scalar Schrödinger equation, which has been widely investigated in the literature, see, e.g., [19,34,35,40,42]. For the case of a bounded domain, system like or similar to (1.1) has been studied by many authors, see [11,7,21,25] and the references therein.…”