On a planar Choquard equation involving exponential critical growth

In this paper, we investigate a class of planar Choquard equation with Riesz potential of logarithm type and the potential V and the weights K, Q decaying to zero at infinity. We prove a weighted Sobolev embedding and a weighted Trudinger–Moser type inequality using a convenient decomposition. These results allow us to address, via variational methods, the existence of solutions to the Choquard equation when the nonlinearities possess critical exponential growth in the Trudinger–Moser sense.