A guide to the Choquard equation

We survey old and recent results dealing with the existence and properties of solutions to the Choquard type equations - Δ u + V ( x ) u = | x | - ( N - α ) ∗ | u | p | u | p - 2 u in R N , and some of its variants and extensions.

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Bibliographic Details
Published in:Fixed point theory and algorithms for sciences and engineering Vol. 19; no. 1; pp. 773 - 813
Main Authors: Moroz, Vitaly, Van Schaftingen, Jean
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.03.2017
Springer Nature B.V
Subjects:
Analysis
Brownian motion
Euclidean space
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Pekar polaron
focusing Hartree equation
attractive nonlocal interaction
Choquard equation
Schrödinger–Newton equation
35Q55 (35R09, 35J91)
Riesz potential
ISSN:1661-7738, 1661-7746, 2730-5422
Online Access:Get full text
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Summary:We survey old and recent results dealing with the existence and properties of solutions to the Choquard type equations - Δ u + V ( x ) u = | x | - ( N - α ) ∗ | u | p | u | p - 2 u in R N , and some of its variants and extensions.
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ISSN:1661-7738
1661-7746
2730-5422
DOI:10.1007/s11784-016-0373-1