Acta Mathematica Sinica, English Series

, Volume 33, Issue 6, pp 761–774

A remark on the existence of entire large and bounded solutions to a (k1, k2)-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 ki-Hessian operator, a1, p1, f1, a2, p2 and f2 are continuous functions.

Keywords

Entire solution large solution elliptic system 

MR(2010) Subject Classification

35J05 35J57 35J60 35J99 

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Applied MathematicsThe Bucharest University of Economic StudiesBucureștiRomania

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