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Ground State Solution for a Class of Choquard Equations Involving General Critical Growth Term

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Abstract

In this paper, we study the nonlinear Choquard equation

$$\begin{aligned} -\Delta {u}+u=\left( |x-y|^{-\mu }*G(u)\right) g(u),\quad \text {in}\ {\mathbb {R}}^N, \end{aligned}$$

where \(0<\mu <\min \{N,4\},\ N\ge 3\), \(g(u)\in {C({\mathbb {R}},{\mathbb {R}})}\) satisfies very general critical growth conditions in the sense of the Hardy–Littlewood–Sobolev inequality and \(G(u)=\int _{0}^{u}g(s){\mathrm{d}}s\). Using the Pohozaev constraint, we find that the above problem admits a ground state solution of Pohozaev type.

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Acknowledgements

H. Chen is supported by the National Natural Science Foundation of China (Grant no. 12071486).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, People’s Republic of China

    He Zhang & Haibo Chen

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  1. He Zhang
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  2. Haibo Chen
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Correspondence to Haibo Chen.

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Communicated by Amin Esfahani.

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Zhang, H., Chen, H. Ground State Solution for a Class of Choquard Equations Involving General Critical Growth Term. Bull. Iran. Math. Soc. 48, 2125–2144 (2022). https://doi.org/10.1007/s41980-021-00624-5

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  • DOI: https://doi.org/10.1007/s41980-021-00624-5

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