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Ground State Solutions for Fractional Choquard Equations with Potential Vanishing at Infinity

Author

Listed:
  • Huxiao Luo

    (Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China)

  • Shengjun Li

    (College of Information Sciences and Technology, Hainan University, Haikou 570228, China)

  • Chunji Li

    (Department of Mathematics, Northeastern University, Shenyang 110004, China)

Abstract

In this paper, we study a class of nonlinear Choquard equation driven by the fractional Laplacian. When the potential function vanishes at infinity, we obtain the existence of a ground state solution for the fractional Choquard equation by using a non-Nehari manifold method. Moreover, in the zero mass case, we obtain a nontrivial solution by using a perturbation method. The results improve upon those in Alves, Figueiredo, and Yang (2015) and Shen, Gao, and Yang (2016).

Suggested Citation

  • Huxiao Luo & Shengjun Li & Chunji Li, 2019. "Ground State Solutions for Fractional Choquard Equations with Potential Vanishing at Infinity," Mathematics, MDPI, vol. 7(2), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:151-:d:203594
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