On a counterexample of Garofalo - Lin for a unique continuation of Schr?dinger equation

摘要

Garofalo and Lin have given a counterexample for which unique continuation fails for the Schr?dinger equation?Δu+c|x|2+?u=0,??>0.Their counterexample consists of a Bessel function of the third kindKv(|x|)with the restriction thatvcannot be an integer. In thisnote we have removed the restriction.