A guide to the Choquard equation

  • Vitaly Moroz
  • Jean Van SchaftingenEmail author


We survey old and recent results dealing with the existence and properties of solutions to the Choquard type equations
$$\begin{aligned} -\Delta u + V(x)u = \left( |x|^{-(N-\alpha )} *|u |^p\right) |u |^{p - 2} u \quad \text {in} \ \mathbb {R}^N, \end{aligned}$$
and some of its variants and extensions.


Choquard equation Pekar polaron Schrödinger–Newton equation focusing Hartree equation attractive nonlocal interaction Riesz potential 

Mathematics Subject Classification

35Q55 (35R09, 35J91) 


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© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Department of MathematicsSwansea UniversitySwanseaWales, UK
  2. 2.Institut de Recherche en Mathématique et PhysiqueUniversité catholique de LouvainLouvain-la-NeuveBelgium

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