具有临界增长的分数阶带有磁场的SchrO¨dinger方程解的多重性
Multiplicity for FractionalSchrO¨dinger Equation with Magnetic Fields and Critical Growth
摘要: 本文研究了下列具有临界增长的含磁场的分数阶Schrödinger方程解的多重性 其中ε > 0 是参数，s∈(0,1)，N≥3 ，(-Δ)As 是分数阶的磁拉普拉斯算子，V∈C(ℝN ,ℝ)和A∈C0,α (ℝN,ℝN),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。
Abstract: In this paper, we investigate the multiplicity for fractional Schrödinger equation with magnetic fields and critical growth where ε > 0 is a parameter, s∈(0,1) , N ≥ 3 ,(-Δ)As is the fractional magnetic Laplacian operators,V ∈C (ℝN ,ℝ) and A∈C0,α (ℝN,ℝN),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.
文章引用：姚安妮. 具有临界增长的分数阶带有磁场的SchrO¨dinger方程解的多重性[J]. 理论数学, 2021, 11(4): 527-538. https://doi.org/10.12677/PM.2021.114066

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