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

Abstract In this paper, we consider the existence of solutions for Choquard equation of the form aligned - u+V (|x|) u =I_ * (Q (|x|) F (u) ) Q (|x|) f (u), \ \ \ \ x R^2, aligned - Δ u + V (| x |) u = I α ∗ (Q (| x |) F (u) ) Q (| x |) f (u), x ∈ R 2, where the nonlinear term f has exponential growth, the radial potentials V, \ Q: R^+ R V, Q: R + → R are 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).