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

In this paper, we study the existence of positive entire large and bounded radial positive solutions for the following nonlinear system

$$left{ {begin{array}{*{20}c}{S_{k_1 } left( {lambda left( {D^2 u_1 } right)} right) + a_1 left( {left| x right|} right)left| {nabla u_1 } right|^{k_1 } = p_1 left( {left| x right|} right)f_1 left( {u_2 } right)} & {for x in mathbb{R}^N ,} {S_{k_2 } left( {lambda left( {D^2 u_2 } right)} right) + a_2 left( {left| x right|} right)left| {nabla u_2 } right|^{k_2 } = p_2 left( {left| x right|} right)f_2 left( {u_1 } right)} & {for x in mathbb{R}^N .} end{array} } right.$$

Here ({S_{{k_i}}}left( {lambda left( {{D^2}{u_i}} right)} right)) is the k _i -Hessian operator, a ₁, p ₁, f ₁, a ₂, p ₂ and f ₂ are continuous functions.