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Ground state solutions of fractional Choquard equations with general potentials and nonlinearities

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In the present paper, we consider the following fractional Choquard equation with general potentials and nonlinearities of the form

$$\begin{aligned} (-\Delta )^{s}u+V(x)u=\Big (I_{\alpha }*F(u)\Big )f(u),~~~\mathrm {in}~{\mathbb {R}}^{N}, \end{aligned}$$

where \(s\in (0,1)\), \(N>2s\), \((-\Delta )^{s}\) is the fractional Laplacian, \(\alpha \in (0,N)\), potential \(V\in C^{1}({\mathbb {R}}^{N},[0,\infty ))\), \(I_{\alpha }\) is a Riesz potential, the nonlinearity F satisfies the general Berestycki–Lions-type assumptions. By introducing some new techniques, we establish the existence of ground state solution of Pohozaev-type to the above equation by variational methods.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, People’s Republic of China

    Zu Gao, Xianhua Tang & Sitong Chen

Authors
  1. Zu Gao
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  2. Xianhua Tang
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  3. Sitong Chen
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Corresponding author

Correspondence to Xianhua Tang.

Additional information

This work is supported by the NNFC (No.: 11571370) of China and and Hunan Provincial Innovation Foundation For Postgraduate (Grant No. CX2017B041).

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Gao, Z., Tang, X. & Chen, S. Ground state solutions of fractional Choquard equations with general potentials and nonlinearities. RACSAM 113, 2037–2057 (2019). https://doi.org/10.1007/s13398-018-0598-5

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  • DOI: https://doi.org/10.1007/s13398-018-0598-5

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