期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 254, 期 8, 页码 3089-3145出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2012.12.019
关键词
Stationary Choquard equation; Stationary focusing Hartree equation; Stationary nonlinear Schrodinger-Newton equation; Riesz potential; Nonlocal semilinear elliptic problem; Exterior domain; Nontrivial nonnegative supersolutions; Ground-state transformation; Decay estimates; Nonlinear Liouville theorems
类别
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 Schrodinger-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. (C) 2013 Elsevier Inc. All rights reserved.
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