Upper and Lower Solution Method for a Singular k‐Hessian System With Augmented Gradient Term

ABSTRACT In this paper, we focus on the existence of solutions for a singular ‐Hessian system with augmented gradient term. By using a radial symmetric transformation and constructing a pair of suitable upper and lower solutions of the singular ‐Hessian system, the existence and the asymptotic estimate of the solution for the system are established under the case where the nonlinearities are allowed to have stronger singularity on the space variables. In particular, the nonsingular case is also considered and a sharp result is derived.