Choquard equations with critical exponential nonlinearities in the zero mass case

TL;DR

This paper studies the existence of positive solutions for Choquard equations with critical exponential nonlinearities in the zero mass case, using variational methods in a limiting Sobolev embedding setting.

Contribution

It extends previous work by considering polynomial kernels and establishing existence results in a challenging limiting case.

Findings

Proved existence of positive solutions under critical exponential growth.

Extended analysis to polynomial kernels beyond logarithmic cases.

Utilized variational methods in a limiting Sobolev embedding context.

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.