Existence and concentration of ground states for a Choquard equation with competing potentials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:465

Article

Zhang, Fubao¹  Zhang, Hui² 

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

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

关键词: Nonlocal nonlinearity;    Concentration;    Competing potential;    Nehari manifold;   

DOI  :  10.1016/j.jmaa.2018.04.065

来源: Elsevier

【 摘 要 】

In this paper, we are concerned with the following Choquard equation in R-3 that -epsilon(2)Delta u + V(x)u =epsilon(mu-3) [(integral(R3) P(y)vertical bar u)y)vertical bar(p)/vertical bar x - y vertical bar(mu)) P(x)vertical bar u vertical bar(p-2) u + (integral(R3) Q(y)vertical bar u)y)vertical bar(q)/vertical bar x - y vertical bar(mu)) Q(x)vertical bar u vertical bar(q-2)], where epsilon > 0 is a parameter, 0 < mu < 3, 6-mu/3 < q < p < 6 - mu, the functions V and P are positive and Q may be sign-changing. Via variational methods, we establish the existence of ground states for small epsilon, and investigate the concentration behavior of ground states and show that they concentrate at a global minimum point of the least energy function as epsilon -> 0. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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