本文研究了下列具有临界增长的含磁场的分数阶Schr？dinger方程解的多重性 $\"\"$ 其中ε > 0 是参数，s∈(0,1)，N≥3 ，(-Δ)_A^s 是分数阶的磁拉普拉斯算子，V∈C(？^N ,？)和A∈C^0,α (？^N,？^N),α∈(0,1]是磁位势。在V的局部条件下以及ε充分小时，本文利用变分方法、截断技巧、Nehari流形方法和Ljusternik-Schnirelmann理论得到了上述方程解的多重性。
In this paper, we investigate the multiplicity for fractional Schr？dinger equation with magnetic fields and critical growth $\"\"$ where ε > 0 is a parameter, s∈(0,1) , N ≥ 3 ,(-Δ)_A^s is the fractional magnetic Laplacian operators,V ∈C (？^N ,？) and A∈C^0,α (？^N,？^N),α ∈(0,1] is magnetic potential.Under a local condition on the potential V and ε is sufficiently small, we obtain some multiplicity results by variational methods, truncated techniques, Nehari manifold method and the Ljusternik-Schnirelmann theory.