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arXiv:1203.3154 [math.AP]AbstractReferencesReviewsResources

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

Vitaly Moroz, Jean Van Schaftingen

Published 2012-03-14Version 1

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 Schroedinger--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 exists.

Comments: 47 pages, 8 figures
Journal: J. Differential Equations 254 (2013), no. 8, 3089-3145
Categories: math.AP
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