Groundstates of nonlinear Choquard equations: Hardy-Littlewood-Sobolev critical exponent

Vitaly Moroz, Jean Van Schaftingen

We consider nonlinear Choquard equation $$ - Δu + V u = \bigl(I_α\ast |u|^{\fracα{N}+1}\bigr) |u|^{\fracα{N}-1} u\quad\text{in (\mathbb{R}^N)},$$ where $N\ge 3$, $V \in L^\infty (…