Existence of radial solutions for k-Hessian system

Abstract

In this paper, we consider the existence of radial solutions to a $ k $-Hessian system in a general form. The existence of radial solutions is obtained under the assumptions that the nonlinearities in the given system satisfy $ k $-superlinear, $ k $-sublinear or $ k $-asymptotically linear at the origin and infinity, respectively. The results presented in this paper generalize some known results. Examples are given for the illustration of the main results.

Keywords

• $ k $-hessian system
• guo-krasnosel'skii fixed point theorem
• existence
• cone