Existence and multiplicity of radial solutions for a k-Hessian system

In this paper, we consider the following nonlinear k-Hessian system {S-k (sigma (D(2)z(1))) = lambda b(vertical bar x vertical bar)phi(-z(1), -z(2)), in Omega, S-k (sigma (D(2)z(2))) = mu h(vertical bar x vertical bar)psi(-z(1), -z(2)), in Omega, z(1) = z(2) = 0, on partial derivative Omega, where lambda, mu > 0, Omega stands for the open unit ball in R-N and S-k(sigma(D(2)z)) is the k-Hessian operator of z. Under the appropriate assumptions on phi and psi, the existence and multiplicity of the k-convex radial solutions are obtained. The method of proving theorems is the Guo-Krasnosel'skii fixed point theorem in a cone. (C) 2022 Elsevier Inc. All rights reserved.