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

By Vitaly Moroz, Jean Van Schaftingen. 2012

109 citations recorded by the source corpus.

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. © 2013 Elsevier Inc.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b691e44bae6a4a87fd260f5e1206f4ec322f19d4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Vitaly Moroz
2. Jean Van Schaftingen
3. Hongyu Ye
4. Minbo Yang
5. Daniele Cassani
6. Jianjun Zhang
7. Claudianor Oliveira Alves
8. Xianhua Tang

In Computational Theory and Mathematics

1. Vitaly Moroz
2. Jean Van Schaftingen
3. Franz Gmeineder
4. Bogdan Raiță
5. Jiankang Xia

In Mathematical Physics

1. Vitaly Moroz
2. Jean Van Schaftingen
3. Hongyu Ye
4. Minbo Yang
5. Jiankang Xia
6. Binlin Zhang
7. Xianhua Tang
8. Claudianor Oliveira Alves

Citations in the corpus

• Semi-classical states for the Choquard equation (2013, background): “We establish a uniform bound on the rescaled mass. for some m = m ( u ε ) > 0 [41, proposition 4.13].”
• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics (2012, unknown): “We have already studied optimal lower bounds of the asymptotics of distributional supersolutions of Choquard equations in exterior domains [24].”