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

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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.


    \begin{equation} \\ \end{equation}
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