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

Abstract

We study the existence of least energy sign-changing solution for the fractional equation $(-Δ)^{s} u=|u|^{2_{s}^{*}-2}u+λf(x,u)$ in a smooth bounded domain $Ω$ of $\mathbb{R}^{N},$ $u=0$ in $\mathbb{R}^{N}\setminus Ω$, where $s\in (0,1)$ and $2_{s}^{*}$ is the fractional critical Sobolev exponent. The proof is based on constrained minimization in a subset of Nehari manifold, containing all the possible sign-changing solutions of the equation.