Limitations on the rate of decrease of solutions of elliptic equations in unbounded domains (Q1123311)

In a recent survey article of \textit{K. F. Barth}, \textit{D. A. Brannan}, and \textit{W. K. Hayman} [Bull. Lond. Math. Soc. 16, 490-517 (1984; Zbl 0593.30001)] the following problem was posed. Given an unbounded domain \(G\subseteq {\mathbb{R}}^ n\) (n\(\geq 2)\), does there exist a positive continuous function \(\delta =\delta (t)\) with the property that any harmonic function u in G satisfying \(| u(x)| <\delta (| x|)\) is necessarily zero? In the present paper, the author gives a positive answer to this (and even a more general) problem.