On nonlocal Choquard equations with Hardy-Littlewood-Sobolev critical exponents
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- 作者：Fashun Gao ; Minbo Yang ; mbyang@zjnu.edu.cn
- 关键词：Choquard equation ; Hardy&ndash ; Littlewood&ndash ; Sobolev critical exponent ; Concave and convex nonlinearities ; Brezis&ndash ; Nirenberg problem
- 刊名：Journal of Mathematical Analysis and Applications
- 出版年：2017
- 出版时间：15 April 2017
- 年：2017
- 卷：448
- 期：2
- 页码：1006-1041
- 全文大小：609 K
- 卷排序：448
文摘
We consider the following nonlinear Choquard equation with Dirichlet boundary condition−Δu=(∫Ω|u|2μ⁎|x−y|μdy)|u|2μ⁎−2u+λf(u)inΩ, where Ω is a smooth bounded domain of RNRN, λ>0λ>0, N≥3N≥3, 0<μ<N0<μ<N and 2μ⁎ is the critical exponent in the sense of the Hardy–Littlewood–Sobolev inequality. Under suitable assumptions on different types of nonlinearities f(u)f(u), we are able to prove some existence and multiplicity results for the equation by variational methods.