期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 263, 期 7, 页码 3943-3988出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2017.05.009
关键词
Choquard equation; Critical growth; Hardy-Littlewood-Sobolev inequality; Semi-classical solutions
类别
资金
- CNPq/Brazil [304036/2013-7]
- NSFC [11571317, 11671364]
- ZJNSF [LY15A010010]
In this paper we study the semiclassical limit for the singularly perturbed Choquard equation -epsilon(2) Delta u + V(x)u = epsilon(mu-3) (integral(R3) Q(y)G(u(y))/vertical bar x-y vertical bar(mu) dy)Q(x)g(u) in R-3, where 0 < mu < 3, s is a positive parameter, V, Q are two continuous real function on R-3 and G is the primitive of g which is of critical growth due to the Hardy-Littlewood-Sobolev inequality. Under suitable assumptions on g, we first establish the existence of ground states for the critical Choquard equation with constant coefficients. Next we establish existence and multiplicity of semi-classical solutions and characterize the concentration behavior by variational methods. (C) 2017 Elsevier Inc. All rights reserved.
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