Infinitely many sign-changing solutions for the Brézis-Nirenberg problem involving the fractional Laplacian

Abstract

In this paper, we consider the following Brézis-Nirenberg problem involving the fractional Laplacian operator: [Equation presented here] where s ∈ (0, 1), Ω is a bounded smooth domain of RN (N > 6s) and 2s∗=2N/N-2s is the critical fractional Sobolev exponent. We show that, for each λ > 0, this problem has infinitely many sign-changing solutions by using a compactness result obtained in [34] and a combination of invariant sets method and Ljusternik-Schnirelman type minimax method.