For every n≥3, the authors construct a nonzero real smooth solution u of -Δu+V u=0 with bounded real V and |u(x)|≤C exp(-c|x|^{4/3}), giving a counterexample to the Landis conjecture in that setting.
Cruz-Sampedro, Unique continuation at infinity of solutions to Schrödinger equations with complex-valued potentials, Proc
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Counterexamples to the Landis conjecture in dimensions three and higher
For every n≥3, the authors construct a nonzero real smooth solution u of -Δu+V u=0 with bounded real V and |u(x)|≤C exp(-c|x|^{4/3}), giving a counterexample to the Landis conjecture in that setting.