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Asymptotic Properties of Ground States to the Choquard Equation with Generalized Autonomous Perturbation

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Abstract

In this article, we study the existence, regularity, and radial symmetry of ground state solution for the Choquard equation with generalized autonomous perturbation

$$\begin{aligned} -\Delta u+\lambda u=\left( \frac{1}{|x|^{N-2}}*|u|^{p} \right) |u|^{p-2}u+g(u) \quad \text {in}~{\mathbb {R}}^N, \end{aligned}$$

where \(\lambda \in {\mathbb {R}}\), \(N\in \{3,4,5\}\), \(p\in \left[ 2,\frac{N+2}{N-2}\right) \), \(g \in C^1({\mathbb {R}})\) satisfies Berestycki-Lions type condition. Further assume that \(p\le \frac{N}{N-2}\), we give the asymptotic behavior (as \(\lambda \rightarrow 0^+\) or \(\lambda \rightarrow +\infty \)) of ground state solutions by using blow-up method.

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  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, Zhejiang, People’s Republic of China

    Huxiao Luo

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Huxiao Luo was supported by the NSFC (No.11901532).

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Luo, H. Asymptotic Properties of Ground States to the Choquard Equation with Generalized Autonomous Perturbation. J Geom Anal 34, 1 (2024). https://doi.org/10.1007/s12220-023-01446-z

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