Degree counting for Toda system with simple singularity: One point blow up
Journal
Journal of Differential Equations
Journal Volume
268
Journal Issue
5
Pages
2163-2209
Date Issued
2020
Author(s)
Abstract
In this paper, we study the degree counting formula of the rank two Toda system with simple singular source when ρ1∈(0,4π)∪(4π,8π) and ρ2∉4πN. The key step is to derive the degree formula of the shadow system, which arises from the bubbling solutions as ρ1 tends to 4π. 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].
Type
journal article