In this paper, we consider the inclusion problems for maximal monotone set-valued vector fields defined on Hadamard manifolds. We discuss the equivalence between nonemptiness of solution set of the inclusion problem and the coercivity condition. The boundedness of solution set of the inclusion problem is studied. An application of our results to optimization problems in Hadamard manifolds is also presented.

中文翻译：

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Hadamard流形中最大单调矢量场包含问题解的存在性和有界性

在本文中，我们考虑了在Hadamard流形上定义的最大单调集值向量场的包含问题。我们讨论了包含问题解集的非空性与矫顽性条件之间的等价性。研究了包含问题解集的有界性。还介绍了我们的结果在Hadamard流形中的优化问题中的应用。