Nevanlinna order of continuous subharmonic functions in an isolated singularity (Q1977855)

The authors study the Nevanlinna order of solutions to the Schrödinger equation \(\Delta u = u\mu\) where \(\mu\) is a positive radial Kato measure on \(\mathbb R^n\), \(n\geq 2\). Using Kelvin's transform they equivalently discuss solutions to \(\Delta u = u\mu\), \(\mu\) a Kato measure on \(\mathbb R^n\setminus \{0\}\) (which may be singular at \(0\)). Then some of the methods developed in connection with the Picard principle can be used and lead to necessary conditions as well as to sufficient conditions for having infinite Nevanlinna order.