We give partial affirmative answers to Landis conjecture in all dimensions for two different types of linear, second order, elliptic operators in a domain Ω⊂ RN. In particular, we provide a sharp decay criterion that ensures when a solution of a nonnegative Schr\"odinger equation in RN with a potential V≤ 1 is trivial. Moreover, we address the analogue of Landis conjecture for quasilinear problems. Our approach relies on the application of Liouville comparison principles and criticality theory.
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Das et al. (2024) studied this question.
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