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On a class of p(x)-Choquard equations with sign-changing potential and upper critical growth

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Abstract

Motived by the Hardy–Littlewood–Sobolev inequality for variable exponents, in this paper we use variational methods to prove the existence of a weak solution for a class of p(x)-Choquard equations with upper critical growth. Using truncation arguments and Krasnoselskii’s genus, we also show a multiplicity of solutions for a class of p(x)-Choquard equations with a nonlocal and non-degenerate Kirchhoff term. Also we show that the solutions obtained belong to \(L^{\infty }({\mathbb {R}}^{N})\) and have polynomial decay.

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Acknowledgements

The author would like to express your sincere gratitude to the anonymous reviewers for their insightful and constructive comments.

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  1. Universidade Federal Rural da Amazônia, campus de Capitão-Poço, Capitão-Poço, PA, Brazil

    B. B. V. Maia

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Maia, B.B.V. On a class of p(x)-Choquard equations with sign-changing potential and upper critical growth. Rend. Circ. Mat. Palermo, II. Ser 70, 1175–1199 (2021). https://doi.org/10.1007/s12215-020-00553-y

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