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math.AP2020★ 30 cited
High energy positive solutions for a coupled Hartree system with Hardy-Littlewood-Sobolev critical exponents
Fashun Gao, Haidong Liu, Vitaly Moroz +1
We study the coupled Hartree system $$ \left\{\begin{array}{ll} -Δu+ V_1(x)u =α_1\big(|x|^{-4}\ast u^{2}\big)u+β\big(|x|^{-4}\ast v^{2}\big)u &\mbox{in}\ \mathbb{R}^N,\\[1mm] -Δv+…
math.AP2020
Nondegeneracy of solutions for a critical Hartree equation
Jacques Giacomoni, Yuanhong Wei, Minbo Yang
The aim of this paper is to prove the nondegeneracy of the unique positive solutions for the following critical Hartree type equations when is close to , $$ -Δu=\left(I_μ\…