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Mathematics 2019, 7(2), 151; https://doi.org/10.3390/math7020151

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

1
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
2
College of Information Sciences and Technology, Hainan University, Haikou 570228, China
3
Department of Mathematics, Northeastern University, Shenyang 110004, China
*
Author to whom correspondence should be addressed.
Received: 8 December 2018 / Revised: 31 January 2019 / Accepted: 1 February 2019 / Published: 5 February 2019
(This article belongs to the Special Issue Polynomials: Theory and Applications)
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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). View Full-Text
Keywords: variational methods; fractional Choquard equation; ground state solution; vanishing potential variational methods; fractional Choquard equation; ground state solution; vanishing potential
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Luo, H.; Li, S.; Li, C. Ground State Solutions for Fractional Choquard Equations with Potential Vanishing at Infinity. Mathematics 2019, 7, 151.

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