ABSTRACT

In this paper, we classify each pair of positive solutions of the following general integral system on half space ${\mathbb{R}}_{+}^n$ $\begin{array}{rl}u\left(y\right)& ={\int }_{{\mathbb{R}}_{+}^n}|x-y{|}^{\nu }f\left(v\right)\left(x\right)\mathrm{d}x,y\in \mathrm{\partial }{\mathbb{R}}_{+}^n\\ v\left(x\right)& ={\int }_{\mathrm{\partial }{\mathbb{R}}_{+}^n}|x-y{|}^{\nu }g\left(u\right)\left(y\right)\mathrm{d}y,x\in {\mathbb{R}}_{+}^n.\end{array}$ The main technique we used is the method of moving sphere.

中文翻译：

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半空间负指数积分系统解的分类

摘要

在本文中，我们在半空间上对以下一般积分系统的每一对正解进行分类${\mathbb{R}}_{+}^n$ $\begin{array}{rl}你\left(\mathrm{是的}\right)& ={\int }_{{\mathbb{R}}_{+}^n}|X-\mathrm{是的}{|}^{\nu }F\left(v\right)\left(X\right)\mathrm{d}X,\mathrm{是的}\in \mathrm{\partial }{\mathbb{R}}_{+}^n\\ v\left(X\right)& ={\int }_{\mathrm{\partial }{\mathbb{R}}_{+}^n}|X-\mathrm{是的}{|}^{\nu }G\left(你\right)\left(\mathrm{是的}\right)\mathrm{d}\mathrm{是的},X\in {\mathbb{R}}_{+}^n.\end{array}$我们使用的主要技术是移动球体的方法。