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 inFixed 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
LanguageEnglish
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
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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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:1661-7738
1661-7746
2730-5422
DOI:10.1007/s11784-016-0373-1