Isolated singularities of the Schrödinger equation with a good potential

Authors:
Juan Luis Vázquez and Cecilia Yarur

Journal:
Trans. Amer. Math. Soc. **315** (1989), 711-720

MSC:
Primary 35J10; Secondary 35B05, 81C05

MathSciNet review:
932451

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Abstract | References | Similar Articles | Additional Information

Abstract: We study the behaviour near an isolated singularity, say 0, of nonnegative solutions of the Schrödinger equation defined in a punctured ball . We prove that whenever the potential belongs to the Kato class the following alternative, well known in the case of harmonic functions, holds: either has a positive limit as or is continuous at 0. In the first case solves the equation in . We discuss the optimality of the class and extend the result to solutions of .

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DOI:
https://doi.org/10.1090/S0002-9947-1989-0932451-0

Keywords:
Isolated singularities,
Schrödinger equation,
Kato potentials

Article copyright:
© Copyright 1989
American Mathematical Society