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Mediterranean Journal of Mathematics

, Volume 12, Issue 3, pp 839–850 | Cite as

Existence and Concentration of Solutions for a Nonlinear Choquard Equation

  • Dengfeng Lü
Article

Abstract

In this paper, we consider the nonlinear Choquard equation
$$-\Delta u+(1 + \mu g(x))u = (K_{\alpha}(x) * |u|^{p} ) |u|^{p-2}u, \ \ \ x \in \mathbb{R}^{N},$$
where \({N \geq 3}\) , \({\alpha \in (0, N)}\) , \({p \in (\frac{N+\alpha}{N}, \frac{N+\alpha}{N-2})}\) , \({\mu > 0}\) is a parameter, \({K_{\alpha}(x)}\) is the Riesz potential and g(x) is a nonnegative continuous potential. Under some assumptions on g(x), we obtain the existence of ground state solutions and concentration results by using the critical point theory.

Mathematics Subject Classification (2010)

35J60 35Q55 35B38 

Keywords

Nonlinear Choquard equation Critical point theory Ground state solution Concentration behavior 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsHubei Engineering UniversityXiaoganPeople’s Republic of China

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