Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (3): 749-759.

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Existence of Positive Ground State Solutions for the Choquard Equation

Xudong Shang1,*(),Jihui Zhang2()   

  1. 1 School of Mathematics, Nanjing Normal University Taizhou College, Jiangsu Taizhou 225300
    2 School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023
  • Received:2021-07-06 Online:2022-06-26 Published:2022-05-09
  • Contact: Xudong Shang;
  • Supported by:
    the NSFC(11601234);the NSFC(11571176);the NSF of Jiangsu Province(BK20160571)


In this paper we study the following nonlinear Choquard equation where $N \geq 3$, $\alpha \in (0, N)$, $I_{\alpha}$ is the Riesz potential, $V(x):\mathbb{R} ^{N} \rightarrow \mathbb{R} $ is a given potential function, and $F\in {\cal C}^{1}(\mathbb{R}, \mathbb{R})$ with $F'(s)=f(s)$. Under assumptions on $V$ and $f$, we do not require the $(AR)$ condition of $f$, the existence of ground state solutions are obtained via variational methods.

Key words: Choquard equation, Ground state solution, Variational methods

CLC Number: 

  • O175.2