EXISTENCE OF A NONTRIVIAL SOLUTION FOR CHOQUARD'S EQUATION

O1; In this article, the authors consider the existence of a nontrivial solution for the following equation:-△u + u = q(x)(|u|2 * 1/|x|)u, x ∈ R3,where q(x) satisfies some conditions. Using a Min-Max method, the authors prove that there is at least one nontrivial solution for the above equation.

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Bibliographic Details
Published inActa Mathematica Scientia Vol. 26; no. 3; pp. 460 - 468
Main Authors Zhang, Zhengjie, Tassilo, Küpper, Hu, Ailian, Xia, Hongqiang
Format Journal Article
LanguageEnglish
Published 01.07.2006
Subjects
Choquard's equation
Min-Max
Existence
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Summary:O1; In this article, the authors consider the existence of a nontrivial solution for the following equation:-△u + u = q(x)(|u|2 * 1/|x|)u, x ∈ R3,where q(x) satisfies some conditions. Using a Min-Max method, the authors prove that there is at least one nontrivial solution for the above equation.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0252-9602
1003-3998
DOI:10.1016/S0252-9602(06)60070-2