| Abstract: |
| In this paper, we consider a Br\`{e}zis-Nirenberg problem involving the fractional Laplacian operator $(-\Delta)^s$ on a bounded smooth domain of $\mathbb{R}^{N}$ ($N>6s$) and $2_s^{*}=\frac{2N}{N-2s}$ is the critical fractional Sobolev exponent. We show that, for each $\lambda>0$, this problem has infinitely many sign-changing solutions by using a compactness result obtained in [S. Yan, J. Yang and X. Yu 2016 JFA] and a combination of invariant sets method and Ljusternik-Schnirelman type minimax method. |
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