A remark on the existence of entire large and bounded solutions to a (k1,k2)-Hessian system with gradient term

TL;DR

This paper investigates conditions under which positive entire large and bounded radial solutions exist for a specific nonlinear (k1,k2)-Hessian system with gradient terms, addressing an open question in the field.

Contribution

It provides new existence results for positive solutions to a (k1,k2)-Hessian system with gradient terms, answering previously open questions.

Findings

Existence of positive entire large solutions established.

Existence of bounded solutions demonstrated.

Results extend understanding of (k1,k2)-Hessian systems with gradient terms.

Abstract

In this paper, we study the existence of positive entire large and bounded radial positive solutions for a nonlinear system. Our results give an answer of the question raised in [11].