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In this work, the following fractional Laplacian problem with pure criticalnonlinearity is considered \begin{equation*} \left\{ \begin{array}{ll}(-\Delta)^{s} u=|u|^{\frac{4s}{N-2s}}u, &\mbox{in}\ \mathbb{R}^N, \\ u\in\mathcal{D}^{s,2}(\mathbb{R}^N), \end{array} \right. \end{equation*} where$s\in (0,1)$, $N$ is a positive integer with $N\geq 3$, $(-\Delta)^{s}$ is thefractional Laplacian operator. We will prove that this problem has infinitelymany non-radial sign-changing solutions.

Infinitely many non-radial sign-changing solutions for a Fractional Laplacian equation with critical nonlinearity