Asymptotically linear Dirac-harmonic maps into flat tori
Asymptotically linear Dirac-harmonic maps into flat tori
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DOI：
10.1016/j.difgeo.2020.101716
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发表时间：
2021-04
影响因子：
0.5
通讯作者：
T. Isobe
中科院分区：
文献类型：
--
作者：
T. Isobe
本文研究了摄动Dirac调和映射到平坦环面的存在性和紧性问题。我们考虑了两种类型的渐近线性摄动，非共振和共振情况。对于非共振情形，我们证明了给定的自由同伦类中的解集是紧的，并且每个自由同伦类中至少存在(n+1)-不同解，其中n是环面的维度。对于共振情形，我们在Landsman-Lazer类型条件下证明了类似的存在性结果。
This paper is concerned with the existence and compactness problems of perturbed Dirac-harmonic maps into flat tori. We consider two types of asymptotically linear perturbations, non-resonance and resonance cases. For the non-resonance case, we show that the set of solutions in a given free homotopy class is compact and there exist at least (n+ 1)-distinct solutions in each free homotopy class, where n is the dimension of the tori. For the resonance case, we prove a similar existence result under Landsman-Lazer type conditions.