In this paper, we consider the iterative properties of solution for a general singular $n$-Hessian equation with decreasing nonlinearity. By introducing a double iterative technique, we firstly establish the criterion of the existence for unique solution, and then study the convergence properties of solution as well as error estimation and the convergence rate between iterative value and exact solution. Different from the existing work, the nonlinear term here is a non-increasing function with high singularity at some time and space variables.

中文翻译：

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一般奇异解的迭代性质 $ñ$-非线性非线性的Hessian方程

在本文中，我们考虑了广义奇异解的迭代性质 $ñ$非线性递减的-Hessian方程。通过引入双重迭代技术，首先建立唯一解存在性的判据，然后研究解的收敛性，误差估计以及迭代值与精确解的收敛速度。与现有工作不同，此处的非线性项是在某些时间和空间变量下具有高奇异性的非递增函数。