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Pure Mathematics 2021
具有临界增长的分数阶带有磁场的SchrO¨dinger方程解的多重性
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Abstract:
![\"\"](\"Edit_bbde02b1-8eb5-4db7-952f-37ace3c38b7e.png\")
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(？N ,？)和A∈C0,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。![\"\"](\"Edit_71cd5a98-f561-4395-8517-824f31b56966.png\")
where ε > 0 is a parameter, s∈(0,1) , N ≥ 3 ,(-Δ)As is the fractional magnetic Laplacian operators,V ∈C (？N ,？) and A∈C0,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.| [1] | Griffiths, D. (2004) Introduction to Quantum Mechanics. 2nd Edition, Prentice Hall, Upper Saddle River, 1-2. |
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