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Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 3, Pages 259-261

On a counterexample of Garofalo - Lin for a unique continuation of Schrödinger equation

Departrnent of Mathematical Sciences, Rutgers University-Camden, Camden 08102, N. J. , USA

Received 1 October 1990; Revised 1 January 1991

Copyright © 1991 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Garofalo and Lin have given a counterexample for which unique continuation fails for the Schrödinger equation Δu+c|x|2+ϵu=0, ϵ>0.

Their counterexample consists of a Bessel function of the third kind Kv(|x|) with the restriction that v cannot be an integer. In this note we have removed the restriction.