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Brouwer degree for Kazdan-Warner equations on a connected finite graph

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 نشر من قبل Liuquan Wang
 تاريخ النشر 2021
  مجال البحث
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We study Kazdan-Warner equations on a connected finite graph via the method of the degree theory. Firstly, we prove that all solutions to the Kazdan-Warner 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 Kazdan-Warner equation on a connected finite graph.



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