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+…