Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains

We consider a semilinear elliptic problem with a nonlinear term which is the product of a power and the Riesz potential of a power. This family of equations includes the Choquard or nonlinear Schrödinger–Newton equation. We show that for some values of the parameters the equation does not have nontr...

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Bibliographic Details
Published in:Journal of Differential Equations 2013-04, Vol.254 (8), p.3089-3145
Main Authors: Moroz, Vitaly, Van Schaftingen, Jean
Format: Article
Language:English
Subjects:
Decay estimates
Exterior domain
Ground-state transformation
Nonlinear Liouville theorems
Nonlocal semilinear elliptic problem
Nontrivial nonnegative supersolutions
Riesz potential
Stationary Choquard equation
Stationary focusing Hartree equation
Stationary nonlinear Schrödinger–Newton equation
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Summary:We consider a semilinear elliptic problem with a nonlinear term which is the product of a power and the Riesz potential of a power. This family of equations includes the Choquard or nonlinear Schrödinger–Newton equation. We show that for some values of the parameters the equation does not have nontrivial nonnegative supersolutions in exterior domains. The same techniques yield optimal decay rates when supersolutions exist.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2012.12.019