A general Phragmén-Lindelöf principle for weak solutions of the Schrödinger equation and its applications

In this paper, we prove a general Phragmén-Lindelöf principle for weak solutions of the Schrödinger equation in unbounded domains (open, connected sets) in Rn(n≥2). As applications, we shall show some similar results, including the Phragmén-Lindelöf principle for solutions of the Schrödinger equation in a cylinder, can be obtained as special cases of the general result.