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

Moroz, Vitaly;Van Schaftingen, Jean
(2013) Journal of Differential Equations — Vol. 254, n° 8, p. 3089-3145 (2013)

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Abstract
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. © 2013 Elsevier Inc.
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Moroz, V., & Van Schaftingen, J. (2013). Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains. Journal of Differential Equations, 254(8), 3089-3145. https://doi.org/10.1016/j.jde.2012.12.019 (Original work published 2013)