Journal of Guangxi Normal University(Natural Science Edition) ›› 2026, Vol. 44 ›› Issue (3): 121-127.doi: 10.16088/j.issn.1001-6600.2025072302

• Mathematics • Previous Articles     Next Articles

Brouwer Degree for Toda System with Nonnegative Prescribed Functions on a Finite Graph

ZHANG Lian, JIANG Zuohai*   

  1. School of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541006, China
  • Received:2025-07-23 Revised:2025-09-03 Online:2026-05-05 Published:2026-05-13

Abstract: This paper investigates the Toda system on connected finite graphs using degree theory. It is proven that all solutions of the Toda system with nonnegative prescribed functions are uniformly bounded, which implies that the Brouwer degree of such a Toda system is well-defined. By the homotopy invariance, the Brouwer degree of the Toda system with nonnegative prescribed functions is shown to be equal to 1. As a corollary, this suggests that the Toda system with nonnegative prescribed functions is solvable.

Key words: finite graphs, Toda system, nonnegative prescribed functions, Brouwer degree, solvability

CLC Number:  O175.25
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