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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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