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Ground states for asymptotically periodic fractional Kirchhoff equation with critical Sobolev exponent

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    * Corresponding author 

The first author is supported by China Scholarship Council (201806370022), Hunan Provincial Innovation Foundation for Postgraduate (CX2018B052). The second author is supported by National Natural Science Foundation of China (11571370)

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  • In this paper, we study the following fractional Kirchhoff equation with critical nonlinearity

    $ \Big(a+b\int_{\mathbb{R}^3}| (-\Delta)^{\frac{s}{2}} u|^2dx\Big) (-\Delta )^su+V(x) u = K(x)|u|^{2_s^*-2}u+\lambda g(x,u), \; \text{in}\; \mathbb{R}^3, $

    where $ a,b>0 $, $ \lambda>0 $, $ (-\Delta )^s $ is the fractional Laplace operator with $ s\in(\frac{3}{4},1) $ and $ 2_s^* = \frac{6}{3-2s} $, $ V,K $ and $ g $ are asymptotically periodic in $ x $. The existence of a positive ground state solution is obtained by variational method.

    Mathematics Subject Classification: 35R11, 35B33, 35A15, 47G20.

    Citation:

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