For radial potentials with arbitrary growth, any real-valued solution of Δu=Vu with u(0)≠0 has a sequence of points where |u(x)|≥c e^{-β(|x|)}, with β explicit in terms of the growth bound.
Davey, On Landis’ Conjecture in the Plane for Potentials with Growth , Viet
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Unique continuation at infinity for potentials with arbitrary radial growth
For radial potentials with arbitrary growth, any real-valued solution of Δu=Vu with u(0)≠0 has a sequence of points where |u(x)|≥c e^{-β(|x|)}, with β explicit in terms of the growth bound.