Sign-changing and signed solutions for fractional Laplacian equations with critical or supercritical nonlinearity

In this paper, we investigate the existence of sign-changing and signed solutions for nonlinear elliptic equations driven by nonlocal integro-differential operators with critical or supercritical nonlinearity. By combining an appropriate truncation argument with a constrained minimization method and the Moser iteration method, we obtain a sign-changing solution and a signed solution for them under some suitable assumptions. As a particular case, we drive an existence theorem of sign-changing and signed solutions for the fractional Laplacian equations with critical or supercritical growth.