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

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

2012-03-14

arxiv.org/abs/1203.3154v1

Mathematics

Analysis of PDEs

47 pages, 8 figures

Scientific paper

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.

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