(untitled) (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we are dedicated to studying the following singularly Choquard equation −ε^2∆u + V (x)u = ε^−α [I_α ∗ F(u)] f(u), x ∈ R^ 2, where V (x) is a continuous real function on R^2, I_α : R^2 → R is the Riesz potential, and F is the primitive function of nonlinearity f which has critical exponential growth. Using the Trudinger-Moser inequality and some delicate estimates, we show that the above problem admits at least one semiclassical ground state solution, for ε > 0 small provided that V (x) is periodic in x or asymptotically linear as |x| → ∞. In particular, a precise and fine lower bound of f(t)e^β_0 t^2 near infinity is introduced in this paper.