On the Kirchhoff type Choquard problem with Hardy-Littlewood-Sobolev critical exponent

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:488

Article

Rui, Jie¹ 

[1] China Univ Petr, Coll Sci, Qingdao 266580, Shandong, Peoples R China

关键词: Kirchhoff type Choquard problem;    Hardy-Littlewood-Sobolev critical exponent;    Variational method;   

DOI  :  10.1016/j.jmaa.2020.124075

来源: Elsevier

【 摘 要 】

In this paper, we study the following Kirchhoff type Choquard problem: -(a + b integral R-N vertical bar del u vertical bar(2)dx)Delta u + u = (integral R-N beta F(u(y) + vertical bar u(y)vertical bar(2)(mu)*/vertical bar x - y vertical bar(mu)dy) x (beta f(u) + 2(mu)*vertical bar u vertical bar 2(mu)*-2(u)) in R-N, (0.1) where N >= 3, a, b > 0 are constants, beta > 0 is a parameter. When mu is an element of (0,4], under suitable conditions on b, beta and f, we prove that (0.1) has a ground state solution. When mu > 4, we also obtain some related existence results. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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