On nonlocal Choquard equations with Hardy-Littlewood-Sobolev critical exponents

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:448

Article

Gao, Fashun¹  Yang, Minbo¹ 

[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

关键词: Choquard equation;    Hardy-Littlewood-Sobolev critical exponent;    Concave and convex nonlinearities;    Brezis-Nirenberg problem;   

DOI  :  10.1016/j.jmaa.2016.11.015

来源: Elsevier

【 摘 要 】

We consider the following nonlinear Choquard equation with Dirichlet boundary condition -Delta u = (integral(Omega) vertical bar u vertical bar(2*)(mu)/vertical bar x - y vertical bar(mu) dy) vertical bar u vertical bar(2)(mu)*(-2)u + lambda f(u) in Omega, where Omega is a smooth bounded domain of R-N, lambda > 0, N >= 3, 0 < mu < N and 2(mu)*, is the critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality. Under suitable assumptions on different types of nonlinearities f(u), we are able to prove some existence and multiplicity results for the equation by variational methods. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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