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We study the existence of least energy sign-changing solution for thefractional equation $(-\Delta)^{s} u=|u|^{2_{s}^{*}-2}u+\lambda f(x,u)$ in asmooth bounded domain $\Omega$ of $\mathbb{R}^{N},$ $u=0$ in$\mathbb{R}^{N}\setminus \Omega$, where $s\in (0,1)$ and $2_{s}^{*}$ is thefractional critical Sobolev exponent. The proof is based on constrainedminimization in a subset of Nehari manifold, containing all the possiblesign-changing solutions of the equation.

Existence of sign-changing solution for a problem involving the fractional Laplacian with critical growth nonlinearities