We study the fractional Schrödinger–Poisson system with critical Sobolev exponent
where denotes the fractional Laplacian of order ; , and are -periodic in the -variables; is the fractional critical Sobolev exponent in dimension . Under some weaker conditions on , we prove the existence of ground state solutions for such a system via the mountain pass theorem in combination with the concentration-compactness principle. Our results are new even for .
"Ground state solutions for the periodic fractional Schrödinger–Poisson systems with critical Sobolev exponent." Rocky Mountain J. Math. 50 (2) 719 - 732, April 2020. https://doi.org/10.1216/rmj.2020.50.719