This is the continuation of our previous work [5], where we introduced and studied some nonlinear integral equations on bounded domains that are related to the sharp Hardy-Littlewood-Sobolev inequality. In this paper, we introduce some nonlinear integral equations on bounded domains that are related to the sharp reversed Hardy-Littlewood-Sobolev inequality. These are integral equations with nonlinear term involving negative exponents. Existence results as well as nonexistence results are obtained.

中文翻译：

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有界域上的负幂非线性积分方程

这是我们之前工作的延续 [5]，我们在那里介绍并研究了一些与尖锐的 Hardy-Littlewood-Sobolev 不等式相关的有界域上的非线性积分方程。在本文中，我们介绍了一些与急剧反转的 Hardy-Littlewood-Sobolev 不等式相关的有界域上的非线性积分方程。这些是包含负指数的非线性项的积分方程。获得存在结果以及不存在结果。