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 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 the existence of a positive solution by variational methods, complementing the analysis in [32], where the case of a logarithmic kernel was considered.

Keywords

• choquard equation
• zero mass
• exponential growth
• variational methods
• limiting sobolev embeddings