Least energy solutions for Choquard equations involving vanishing potentials and exponential growth

In this paper, we consider the existence of solutions for Choquard equation of the form −?u + V(|x|)u = [Iα ∗ (Q(|x|)F(u))]Q(|x|) f (u), x ∈ R2, where the nonlinear term f has exponential growth, the radial potentials V, Q : R
+ → Rare unbounded, singular at the origin or decaying to zero. By combining the variational methods, Trudinger-Moser inequality and some new approaches to estimate precisely the minimax level of the energy functional, we prove the existence of a nontrivial solution for the above problem under some weaker assumptions. Our study extends and improves the results of [Albuquerque-Ferreira-Severo, Milan J. Math. 89 (2021)] and [Alves-Shen, J. Differential Equations, 344 (2023)].