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

Huxiao Luo, Shengjun Li and Chunji Li
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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

Mathematics, 2019, vol. 7, issue 2, 1-17

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).

Keywords: variational methods; fractional Choquard equation; ground state solution; vanishing potential (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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