Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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EXISTENCE AND UNIQUENESS OF SOLUTIONS TO THE BOGOMOL’NYI EQUATION ON GRAPHS

  • Yuanyang Hu (School of Mathematics and Statistics Henan University and School of Science and Technology University of New England)
  • Received : 2025.05.28
  • Accepted : 2025.12.24
  • Published : 2026.08.01
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Abstract

Let G = (V, E) be a connected finite graph. We study the Bogomol'nyi equation $${\Delta}u=e^u-4{\pi}{\sum_{s=1}^k}n_s{\delta}_{z_s}\;on\;G,$$, where z1, z2, . . . , zk are arbitrarily chosen distinct vertices on the graph, nj is a positive integer, j = 1, 2, . . . , k and 𝛿zs is the Dirac mass at zs. We obtain a necessary and sufficient condition for the existence and uniqueness of solutions to the Bogomol'nyi equation.

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Acknowledgement

This work is supported by the National Natural Science Foundation of China (Grant No. 12201184).