Year: 2014
Type: preprint
Abstract: Here we initiate the program for computing the Leray-Schauder topological degree for $SU(3)$ Toda system. This program still contains a lot of challenging problems for analysts. The first step of our approach is to answer whether concentration phenomena holds or not. In this paper, we prove the concentration phenomena holds while $ρ_1$ crosses $4π$, and $ρ_2\notin 4π\mathbb{N}$. However, for $ρ_1\geq 8π$, the question whether concentration holds or not still remains open up to now. The second step is to study the corresponding shadow system and its degree counting formula. The last step is to construct bubbling solution of $SU(3)$ Toda system via a non-degenerate solution of the shadow system. Using this construction, we succeed to calculate the degree for $ρ_1\in(0,4π)\cup(4π,8π)$ and $ρ_2\notin 4π\mathbb{N}$.
Source: arXiv (Cornell University)
Authors: Lin, Chang-Shou, Wei, Juncheng, Yang, Wen
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1774097103