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Research Article | Open Access

Choquard equations with critical exponential nonlinearities in the zero mass case

Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell'Insubria, RISM-Riemann International School of Mathematics, Villa Toeplitz, Via G.B. Vico, 46-21100 Varese, Italy
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Abstract

We investigate Choquard equations in RN 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 equationzero massexponential growthvariational methodslimiting Sobolev embeddings
CLC number: 35A15, 35J20, 35J60, 35B33

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AIMS Mathematics
Volume 9 Issue 8,
August 2024
Pages 21538-21556
DOI: 10.3934/math.20241046

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Romani G. Choquard equations with critical exponential nonlinearities in the zero mass case. AIMS Mathematics, 2024, 9(8): 21538-21556. https://doi.org/10.3934/math.20241046

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Received: 24 April 2024
Revised: 17 June 2024
Accepted: 19 June 2024
Published: 15 August 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)