On the solutions to weakly coupled system of Πki-Hessian equations

This paper investigates the nontrivial k -admissible radial solutions for a weakly coupled system of Π k i -Hessian equations subject to Dirichlet boundary conditions on the unit ball. By employing fixed point theory in a cone and decoupling techniques, we establish the sufficient conditions for the existence and multiplicity of nontrivial k -admissible radial solutions. For power-type weakly coupled systems, we also obtain uniqueness and nonexistence results for nontrivial k -admissible radial solutions. Finally, we provide an example of 4-coupled system that simultaneously incorporates the classical Laplacian, the Monge-Ampère operator, the Π 2 -Hessian operators, and the ( N − 1 ) Monge-Ampère operator.