# American Institute of Mathematical Sciences

January  2020, 19(1): 123-144. doi: 10.3934/cpaa.2020008

## Ground states of nonlinear fractional Choquard equations with Hardy-Littlewood-Sobolev critical growth

 1 College of Science, China University of Mining and Technology, Xuzhou 221116, China 2 College of Mathematica and Statistics, Chongqing Jiaotong University, Chongqing 400074, China

* Corresponding author

Received  October 2018 Revised  May 2019 Published  July 2019

We are concerned with nonlinear fractional Choquard equations involving critical growth in the sense of the Hardy-Littlewood-Sobolev inequality. Without the Ambrosetti-Rabinowitz condition or monotonicity condition on the nonlinearity, we establish the existence of radially symmetric ground state solutions.

Citation: Hua Jin, Wenbin Liu, Huixing Zhang, Jianjun Zhang. Ground states of nonlinear fractional Choquard equations with Hardy-Littlewood-Sobolev critical growth. Communications on Pure & Applied Analysis, 2020, 19 (1) : 123-144. doi: 10.3934/cpaa.2020008
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