Choquard equations with critical exponential nonlinearities in the zero mass case

Giulio Romani; Giulio Romani

doi:10.3934/math.20241046

AIMS Mathematics

2024, Volume 9, Issue 8: 21538-21556. doi: 10.3934/math.20241046

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Choquard equations with critical exponential nonlinearities in the zero mass case

Giulio Romani ^,

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

Received: 24 April 2024 Revised: 17 June 2024 Accepted: 19 June 2024 Published: 05 July 2024
MSC : 35A15, 35J20, 35J60, 35B33

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.
- Choquard equation,
- zero mass,
- exponential growth,
- variational methods,
- limiting Sobolev embeddings
Citation: Giulio Romani. Choquard equations with critical exponential nonlinearities in the zero mass case[J]. AIMS Mathematics, 2024, 9(8): 21538-21556. doi: 10.3934/math.20241046

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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.

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