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Existence of Solutions for a Critical Choquard–Kirchhoff Problem with Variable Exponents

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Abstract

We consider the Choquard–Kirchhoff problem involving variable exponents and critical nonlinearity in the whole space. Combining the concentration-compactness principle in \(W^{1,p(x)}(\mathbb {R}^N)\), the Hardy–Littlewood–Sobolev type inequality with variable exponents, and the mountain pass theorem, we provide the existence of nontrivial radial solutions for the above problem in nondegenerate and degenerate cases.

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Acknowledgements

This research was partially supported by the National Natural Science Foundation of China (No. 12171486), Natural Science Foundation for Excellent Young Scholars of Hunan Province and Central South University Innovation-Driven Project for Young Scholars (No. 2019CX022).

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Authors and Affiliations

  1. Department of Mathematics, National University of Defense Technology, Changsha, 410073, Hunan, People’s Republic of China

    Youpei Zhang

  2. School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, 410083, Hunan, People’s Republic of China

    Dongdong Qin

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  1. Youpei Zhang
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Correspondence to Dongdong Qin.

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Zhang, Y., Qin, D. Existence of Solutions for a Critical Choquard–Kirchhoff Problem with Variable Exponents. J Geom Anal 33, 200 (2023). https://doi.org/10.1007/s12220-023-01266-1

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  • DOI: https://doi.org/10.1007/s12220-023-01266-1

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