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.