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Liouville theorems for generalized harmonic functions. (English) Zbl 1078.35020
Summary: Each nonzero solution of the stationary Schrödinger equation $$\Delta u(x)-c(r)u(x)=0$$ in $$\mathbb R^n$$ with a nonnegative radial potential c(r) must have certain minimal growth at infinity. If $$r ^2 c(r)=O(1)$$, $$r\to\infty$$, then a solution having power growth at infinity, is a generalized harmonic polynomial.

##### MSC:
 35B40 Asymptotic behavior of solutions to PDEs 31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions 35J10 Schrödinger operator, Schrödinger equation
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