In this paper, we combine a two-step iterative shooting argument and a fixed-point theorem approach to establish the existence of the solution of the dark monopole equations in a recently formulated non-Abelian gauge field theory by Deglmann and Kneipp and discuss its qualitative properties. In addition, the energy-minimizing solution of the dark monopole equations also satisfies the monotonicity, thus settling an unsettled but characteristic issue left out in an existence theorem regarding such a solution and confirming evidence from earlier numerical simulations.

中文翻译：

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非阿贝尔规范场理论中暗单极子方程解的单调性

在本文中，我们结合了两步迭代射击参数和定点定理方法，以建立由Deglmann和Kneipp最近提出的非阿贝尔规范场理论中暗单极子方程解的存在性，并对其定性进行了讨论。特性。另外，暗单极子方程组的最小能量解也满足了单调性，因此解决了关于该解的存在性定理中未解决但尚未解决的特征问题，并从早期的数值模拟中得到了证实。