数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (1): 137-147.doi: 10.1016/S0252-9602(10)60030-6

• 论文 • 上一篇    下一篇

EXISTENCE OF A COOPERATIVE ELLIPTIC SYSTEM INVOLVING PUCCI OPERATOR

杨健夫, 余小辉   

  1. Department of Mathematics, Jiangxi Normal University, Nanchang 330022, China
  • 收稿日期:2007-07-28 修回日期:2007-09-17 出版日期:2010-01-20 发布日期:2010-01-20
  • 基金资助:

    This work is supported by National Natural Sciences Foundations of China (10571175, 10631030).

EXISTENCE OF A COOPERATIVE ELLIPTIC SYSTEM INVOLVING PUCCI OPERATOR

Yang-Jian-Fu, YU Xiao-Hui   

  1. Department of Mathematics, Jiangxi Normal University, Nanchang 330022, China
  • Received:2007-07-28 Revised:2007-09-17 Online:2010-01-20 Published:2010-01-20
  • Supported by:

    This work is supported by National Natural Sciences Foundations of China (10571175, 10631030).

摘要:

The authors study the existence of solutions for the nonlinear elliptic system

{  -M\+λ, ∧(D2u)=f(u, v)   in  Ω,   

   -M\+λ, ∧(D2v)=f(u, v)   in  Ω,   

   u ≥ 0, v ≥ 0                    in  Ω,

   u=v=0                            on  ∂Ω,

where Ω is a bounded convex domain in RN, N ≥ 2. It is shown that under some assumptions on f and g, the problem has at least one  positive solution (u,v).

关键词: fixed point index, nonlinear elliptic system, Pucci operator

Abstract:

The authors study the existence of solutions for the nonlinear elliptic system

{  -M\+λ, ∧(D2u)=f(u, v)   in  Ω,   

   -M\+λ, ∧(D2v)=f(u, v)   in  Ω,   

   u ≥ 0, v ≥ 0                    in  Ω,

   u=v=0                            on  ∂Ω,

where Ω is a bounded convex domain in RN, N ≥ 2. It is shown that under some assumptions on f and g, the problem has at least one  positive solution (u,v).

Key words: fixed point index, nonlinear elliptic system, Pucci operator

中图分类号: 

  • 35J50