Morse homology for asymptotically linear Dirac equations on compact manifolds
Morse homology for asymptotically linear Dirac equations on compact manifolds
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DOI：
10.1016/j.jde.2020.04.007
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发表时间：
2020-09
影响因子：
2.4
通讯作者：
T. Isobe
中科院分区：
文献类型：
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作者：
T. Isobe
给出了紧致流形上渐近线性Dirac方程的莫尔斯（co）同调的构造和计算，这些方程在无穷远处是非共振的，或在无穷远处是共振的，并且满足Landesman-Lazer型条件.对于非共振情形，我们证明了同调只依赖于无穷远线性部分的同伦类，而对于共振情形，（余）同调与扰动项在无穷远退化空间的限制的莫尔斯（余）同调同构.从这些，（共）同源性明确计算。并给出了渐近线性Dirac方程解的存在性的应用。
We give constructions and calculations of Morse (co)homologies for asymptotically linear Dirac equations on compact manifolds which are non-resonance at infinity, or resonance at infinity and satisfy Landesman-Lazer type conditions. For the non-resonance case, we show that the homology depends only on the homotopy class of the linear part at infinity, while for the resonance case, the (co)homology is isomorphic with the Morse (co)homology of the restriction of the perturbation term to the degenerate space at infinity. From these, (co)homologies are explicitly calculated. Applications to the existence of solutions of asymptotically linear Dirac equations is also given.