In this paper, we study some properties of positive solutions of nonlinear integral equations with axis-symmetric kernels, which arise from weak-type convolution-Young’s inequality and the stationary magnetic compressible fluid stars. With the help of the method of moving planes and regularity lifting lemma, we show that all of the positive solutions in certain functional spaces are symmetric and monotonically decreasing on the axis of symmetry, and the integrable interval of positive solutions is also obtained. In addition, by analyzing the decay rates of positive solutions in different directions, we prove that no radial solution is allowed in some weighted functional space.

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关于轴对称核的积分方程

在本文中，我们研究具有轴对称核的非线性积分方程的正解的一些性质，这些性质是由弱型卷积-杨氏不等式和固定的磁性可压缩流体星引起的。借助移动平面和规则提升引理的方法，我们证明了某些功能空间中的所有正解都是对称的，并且在对称轴上单调递减，并且还获得了正解的可积区间。此外，通过分析正解在不同方向上的衰减率，我们证明在某些加权函数空间中不允许径向解。