A remark on the existence of solutions to a (k1,k2)-Hessian system with convection term

TL;DR

This paper establishes new existence results for positive solutions to a nonlinear (k1,k2)-Hessian system with convection terms, providing simplified proofs that enhance previous findings.

Contribution

It introduces two new theorems with concise proofs for positive solutions in a complex Hessian system including convection, improving prior work by Zhang and Zhou.

Findings

Existence of positive entire large solutions confirmed.

Existence of bounded positive solutions established.

Results extend and refine previous research.

Abstract

In this paper, two new results and short proofs are given for the existence of positive entire large and bounded radial positive solutions for a nonlinear system with gradient term. Our results complete and improve a recently work published by Zhang and Zhou. The main difficulty in dealing with our system is the presence of the convection term.