This paper is concerned with a class of uniformly elliptic nonlocal Bellman systems in unbounded Lipschitz domains. There are two major ingredients. The first is a narrow region principle in unbounded domains. We can use this to carry out the direct method of moving planes. The second ingredient is to prove the monotonicity of positive bounded solutions for a cooperative system with uniformly elliptic nonlocal Bellman operators. Without decay assumptions on solutions, we estimate the singular integrals defining the operator along a sequence of approximate minimum points.

中文翻译：

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一类均匀椭圆非局部贝尔曼系统解的单调性

本文关注无界 Lipschitz 域中的一类一致椭圆非局部 Bellman 系统。有两种主要成分。第一个是无界域中的窄域原则。我们可以使用它来执行移动平面的直接方法。第二个要素是证明具有一致椭圆非局部贝尔曼算子的合作系统的正有界解的单调性。在没有对解的衰减假设的情况下，我们沿着一系列近似最小点估计定义算子的奇异积分。