Positive solutions and large time behaviors of Schrödinger semigroups, Simon's problem

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Abstract

Let H = −Δ + V, where V is a multiplication operator by a real-valued function V(x) on Rn which is uniformly Hölder continuous and (1 + ¦x¦2)ϱ2 V(x) ∈ L(Rn) for some ϱ > 4. The relationship between existence of positive solutions, with growth conditions, of Hg = 0 and asymptotic behaviors as t → ∞ of eth is established. Using it B. Simon's problem for H on R2 is solved.

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