JOURNAL OF DIFFERENTIAL EQUATIONS | 卷:268 |
Degree counting for Toda system with simple singularity: One point blow up | |
Article | |
Lee, Youngae1  Lin, Chang-Shou2  Yang, Wen3  Zhang, Lei4  | |
[1] Kyungpook Natl Univ, Teachers Coll, Dept Math Educ, Daegu, South Korea | |
[2] Natl Taiwan Univ, Ctr Adv Study Theoret Sci, Taida Inst Math Sci, Taipei 106, Taiwan | |
[3] Chinese Acad Sci, Wuhan Inst Phys & Math, POB 71010, Wuhan 430071, Hubei, Peoples R China | |
[4] Univ Florida, Dept Math, 358 Little Hall,POB 118105, Gainesville, FL 32611 USA | |
关键词: Toda system; Topological degree; Bubbling solutions; Shadow system; | |
DOI : 10.1016/j.jde.2019.09.016 | |
来源: Elsevier | |
【 摘 要 】
In this paper, we study the degree counting formula of the rank two Toda system with simple singular source when rho(1) is an element of(0, 4 pi) boolean OR(4 pi, 8 pi) and rho(2) is not an element of 4 pi N. The key step is to derive the degree formula of the shadow system, which arises from the bubbling solutions as rho(1) tends to 4 pi. In order to compute the topological degree of the shadow system, we need to find some suitable deformation. During this deformation, we shall deal with new difficulty arising from the phenomenon: blow up does not necessarily imply concentration of mass. This phenomenon occurs due to the collapsing of singularities. This is a continuation of the previous work [25]. (C) 2019 Elsevier Inc. All rights reserved.
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