In this paper, we focus on the uniqueness and iterative properties of solutions for a singular k-Hessian system involving coupled nonlinear terms with different properties. Unlike the existing work, instead of directly dealing with the system, we use a coupled technique to transfer the Hessian system to an integral equation, and then by introducing an iterative technique, the iterative properties of solution are derived including the uniqueness of solution, iterative sequence, the error estimation and the convergence rate as well as entire asymptotic behaviour.
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