This paper is devoted to studying the coupled system of multiparameter k-Hessian equations S_k(\mu(D^2u_1))=\lambda_1\rho_1(|x|)f_1(-u_1,-u_2) in B, S_k(\mu(D^2u_2))=\lambda_2\rho_2(|x|)f_2(-u_1,-u_2) in B, u_1=u_2=0 on \partial B, where B=\{x\in\mathbb{R}^n:|x|<1\}, \lambda_1,\lambda_2 are positive parameters, \rho_i\,(i=1,2) is singular near the boundary \partial B, f_i\,(i=1,2) satisfies a combined superlinear condition at \infty. Employing the fixed point theorem of Krasnosel'skii type in Banach space, the existence and multiplicity of nontrivial radial solutions are established. In particular, the dependence of the solutions on the parameters \lambda_1,\lambda_2 is also discussed. Finally, we study the nonexistence results of nontrivial radial solutions for the case \lambda_1,\lambda_2\gg1.
Mathematics Subject Classification (2010). 34B15, 34B18.