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In this paper, we consider the following Brézis-Nirenberg problem involving the fractional Laplacian operator:(  −  Δ   )  s   u  =  λ  u  +   |   u    |2  s   ∗    −  2    uinΩ  ,u  =  0on∂  Ω  ,$$\begin{array}{} \displaystyle\left\{\begin{array}{ll}    (-\Delta)^s u=\lambda u+|u|^{2_s^{*}-2}u &amp; \textrm{in}\ \, \Omega, \\    u=0   &amp; \textrm{on}\ \, \partial\Omega,  \end{array}  \right.  \end{array} $$

Infinitely many sign-changing solutions for the Brézis-Nirenberg problem involving the fractional Laplacian