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A remark on the existence of entire large and bounded solutions to a (k 1, k 2)-Hessian system with gradient term

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Abstract

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.

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We thank the referees for their time and comments.

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  1. Department of Applied Mathematics, The Bucharest University of Economic Studies, Piata Romana, 1st district, 010374, postal office: 22, București, Romania

    Dragos Patru Covei

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  1. Dragos Patru Covei
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Correspondence to Dragos Patru Covei.

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Covei, D.P. A remark on the existence of entire large and bounded solutions to a (k 1, k 2)-Hessian system with gradient term. Acta. Math. Sin.-English Ser. 33, 761–774 (2017). https://doi.org/10.1007/s10114-017-6291-3

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