Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590485 | Journal of Functional Analysis | 2013 | 32 Pages |
Abstract
We consider a semilinear elliptic problem−Δu+u=(Iα⁎|u|p)|u|p−2uinRN, where IαIα is a Riesz potential and p>1p>1. This family of equations includes the Choquard or nonlinear Schrödinger–Newton equation. For an optimal range of parameters we prove the existence of a positive groundstate solution of the equation. We also establish regularity and positivity of the groundstates and prove that all positive groundstates are radially symmetric and monotone decaying about some point. Finally, we derive the decay asymptotics at infinity of the groundstates.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Vitaly Moroz, Jean Van Schaftingen,