Positive Radial Solutions to the Double Singular \(k_i\)-Hessian System: Existence, Multiplicity and Dependence on a Parameter

In this paper, the author is concerned with the positive radial solutions for a double singular \(k_i\) $k_i$ -Hessian system with a parameter \(\lambda \) $\lambda$ . We establish a criterion on the existence of a positive radial solution for small \(\lambda \) $\lambda$ , a criterion on the multiplicity of positive radial solutions for certain ranges of \(\lambda \) $\lambda$ , and a criterion on the nonexistence of positive radial solutions in the case \(\lambda \gg 1\) $\lambda \gg 1$ . The dependence of the positive radial solution on the parameter \(\lambda \) $\lambda$ is also studied.