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Schrödinger equations with unique positive isolated singularities

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Abstract

We investigate the class of nonnegative potentialsV(x) for which the Schrödinger equation −Δu+V u=0 admits a unique type of singular solution such thatu(x)→∞ asx→0. This class includes the potentials with inverse-square growth at 0, i.e. 0≤V(x)≤C|x|−2. If for instance we fix boundary datau=g at |x|=1 then the singular solution is unique up to a multiplicative factor.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049, Madrid, Spain

    Juan Luis Vazquez

  2. Universidad de Santiago de Chile, Correo 2, 56-59, Casilla, Santiago De Chile

    Cecilia Yarur

Authors
  1. Juan Luis Vazquez
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  2. Cecilia Yarur
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Vazquez, J.L., Yarur, C. Schrödinger equations with unique positive isolated singularities. Manuscripta Math 67, 143–163 (1990). https://doi.org/10.1007/BF02568427

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  • DOI: https://doi.org/10.1007/BF02568427

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