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

Abstract

In this work, the following fractional Laplacian problem with pure critical nonlinearity 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 the fractional Laplacian operator. We will prove that this problem has infinitely many non-radial sign-changing solutions.