Multiplicity and concentration of solutions for Choquard equations with critical growth

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:481

Article

Zhang, Hui¹  Zhang, Fubao² 

[1] Jinling Inst Technol, Dept Math, Nanjing 211169, Jiangsu, Peoples R China

[2] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China

关键词: Variational method;    Choquard equation;    Semiclassical state;    Critical growth;   

DOI  :  10.1016/j.jmaa.2019.123457

来源: Elsevier

【 摘 要 】

In this paper, we are concerned with the Choquard equation -epsilon(2)Delta u+V(x)u = epsilon(mu-3) integral(R3)vertical bar u(y)vertical bar(6-mu) + Q(y)F(u(y))/vertical bar x - y vertical bar(mu)dy(vertical bar u vertical bar(4-mu)u+Q(x)f(u)/6 - mu) in R-3, where epsilon > 0 is a parameter, 0 < mu < 3, 6 - mu is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality in R-3, V and Q are bounded continuous functions, f is a continuous subcritical term, and F is the primitive function of f. By variational methods, we establish the existence and concentration of positive ground states and investigate the relation between the number of solutions and the topology of the set where V attains its global minimum and Q attains its global maximum. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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