A Liouville-type theorem for Schrödinger equations with nonnegative potential

Henrik Ueberschaer

Let $u$ be a solution of $\Delta u=Vu$ on ${\mathbb{R}}^d$, where $V$ be continuous, nonnegative and bounded. We prove that the condition $${\int }_{r_j\le |x|\le r_j+1}|u(x){|}^{2}dx\to 0,$$ al…