Groundstates for magnetic Choquard equations with critical exponential growth

This paper is dedicated to show the existence of ground state solution for a magnetic Choquard equation with critical exponential growth. By introducing a Moser type function involving magnetic potential and applying analytical techniques, we surmount the obstacles brought from the magnetic potential which makes it a complex-valued problem and the critical exponential growth nonlinearity which makes it difficult to show the non-vanishing of Cerami sequence. Our methods can be applied to related magnetic elliptic equations.