Existence of positive entire radial solutions to a $(k_1,k_2)$-Hessian systems with convection terms

In this article, we prove two new results on the existence of positive entire large and bounded radial solutions for nonlinear system with gradient terms $$\displaylines{ S_{k_1}(\lambda (D^{2}u_1) )+b_1(| x| ) | \nabla u_1|^{k_1} =p_1(| x| ) f_1(u_1,u_2) \quad\text{for }x\in \mathbb{R}^{N}, \cr S_{...

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Bibliographic Details
Published in:Electronic journal of differential equations 2016-10, Vol.2016 (272), p.1-8
Main Author: Dragos-Patru Covei
Format: Article
Language:English
Subjects:
elliptic system
Entire solution
large solution
Online Access:Get full text
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Summary:In this article, we prove two new results on the existence of positive entire large and bounded radial solutions for nonlinear system with gradient terms $$\displaylines{ S_{k_1}(\lambda (D^{2}u_1) )+b_1(| x| ) | \nabla u_1|^{k_1} =p_1(| x| ) f_1(u_1,u_2) \quad\text{for }x\in \mathbb{R}^{N}, \cr S_{k_2}(\lambda (D^{2}u_2) ) +b_2(| x| ) | \nabla u_2|^{k_2} =p_2(| x| ) f_2(u_1,u_2) \quad\text{for }x\in \mathbb{R}^{N}, }$$ where $S_{k_i}(\lambda (D^{2}u_i) ) $ is the $k_i$-Hessian operator, $b_1,p_1, f_1, b_2, p_2,f_2$ are continuous functions satisfying certain properties. Our results expand those by Zhang and Zhou [23]. The main difficulty in dealing with our system is the presence of the convection term.
ISSN:1072-6691