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

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

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 ma...

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Bibliographic Details
Main Authors: Huxiao Luo, Shengjun Li, Chunji Li
Format: Article
Language:English
Published: MDPI AG 2019-02-01
Series:Mathematics
Subjects:
variational methods
fractional Choquard equation
ground state solution
vanishing potential
Online Access:https://www.mdpi.com/2227-7390/7/2/151
Description
Summary: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).
ISSN:2227-7390

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