A general Phragmén-Lindelöf principle for weak solutions of the Schrödinger equation and its applications (Q1693628)

A general form of the Phragmén-Lindelöf principle for weak solutions of the Schrödinger equations in unbounded domains in \(\mathbb{R}^n\) \((n\geq 2)\), namely Theorem 1.1, is proved in this paper. This improves some previous work for equations in a cone by using a generalization of the modified Nevanlinna norm with respect to the Schrödinger operator by the author and \textit{G. Deng} [Glasg. Math. J. 53, No. 3, 599--610 (2011; Zbl 1229.31004)]. Two applications are given, respectively, to the whole space \(\mathbb{R}^n\) and a cylinder.