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Liouville Theorems for Generalized Harmonic Functions

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Abstract

Each nonzero solution of the stationary Schrödinger equation Δu(x)−c(r)u(x)=0 in R n with a nonnegative radial potential c(r) must have certain minimal growth at infinity. If r 2 c(r)=O(1), r→∞, then a solution having power growth at infinity, is a generalized harmonic polynomial.

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Authors and Affiliations

  1. Bronx Community College of the City University of New York, University Avenue, West 181st Street, Bronx, NY, 10453, U.S.A.

    Alexander I. Kheyfits

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  1. Alexander I. Kheyfits
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Kheyfits, A.I. Liouville Theorems for Generalized Harmonic Functions. Potential Analysis 16, 93–101 (2002). https://doi.org/10.1023/A:1024872826453

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