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

Abstract

ABSTRACTIn this paper, we study the existence of sign-changing solution for a non-local problem, involving the fractional Laplacian operator and critical growth nonlinearities, namely where Ω is a bounded smooth domain of , , is the fractional critical Sobolev exponent and λ is a positive parameter. Under certain assumptions on f, we show that the problem has a least-energy sign-changing solution for λ large. The proof is based on constrained minimization in a subset of Nehari manifold, containing all the possible solutions which change sign of this equation.