Brouwer degree for KazdanWarner equations on a connected finite graph
Abstract
We study KazdanWarner equations on a connected finite graph via the method of the degree theory. Firstly, we prove that all solutions to the KazdanWarner equation with nonzero prescribed function are uniformly bounded and the Brouwer degree is well defined. Secondly, we compute the Brouwer degree case by case. As consequences, we give new proofs of some known existence results for the KazdanWarner equation on a connected finite graph.
 Publication:

arXiv eprints
 Pub Date:
 April 2021
 arXiv:
 arXiv:2104.09881
 Bibcode:
 2021arXiv210409881S
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Analysis of PDEs;
 Mathematics  Combinatorics;
 Mathematics  Functional Analysis;
 35R02;
 35A16
 EPrint:
 23 pages