Choquard equations with critical exponential nonlinearities in the zero mass case

Abstract

We investigate Choquard equations in ${\mathbb{R}}^N$ driven by a weighted $N$-Laplace operator and with polynomial kernel and zero mass. Since the setting is limiting for the Sobolev embedding, we work with nonlinearities which may grow up to the critical exponential. We establish existence of a positive solution by variational methods, completing the analysis in [Romani, ArXiv preprint 2023], where the case of a logarithmic kernel was considered.