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.

References in corpus (6)

• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• A guide to the Choquard equation
• Groundstates for Choquard type equations with Hardy-Littlewood-Sobolev lower critical exponent
• Nonlocal planar Schrödinger-Poisson systems in the fractional Sobolev limiting case
• Schrödinger-Poisson systems with zero mass in the Sobolev limiting case
• Nonlinear Schrödinger-Poisson systems in dimension two: the zero mass case

Cited by in corpus (3)

• Positive solutions with prescribed mass for a planar Choquard equation with critical growth
• Schrödinger-Poisson systems with zero mass in the Sobolev limiting case
• Nonlinear Schrödinger-Poisson systems in dimension two: the zero mass case