数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (5): 1363-1379.doi: 10.1007/s10473-019-0514-x

• 论文 • 上一篇    下一篇

BOUNDARY BLOW-UP RATE OF THE LARGE SOLUTION FOR AN ELLIPTIC COOPERATIVE SYSTEM

王影1, 王明新2   

  1. 1. School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450011, China;
    2. Natural Science Research Center, Harbin Institute of Technology, Harbin 150080, China
  • 收稿日期:2017-12-12 修回日期:2018-11-30 出版日期:2019-10-25 发布日期:2019-11-11
  • 通讯作者: Ying WANG E-mail:wy@ncwu.edu.cn
  • 作者简介:Mingxin WANG,E-mail:mxwang@hit.edu.cn
  • 基金资助:
    This work was supported by the National Natural Science Foundation of China (11501199).

BOUNDARY BLOW-UP RATE OF THE LARGE SOLUTION FOR AN ELLIPTIC COOPERATIVE SYSTEM

Ying WANG1, Mingxin WANG2   

  1. 1. School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450011, China;
    2. Natural Science Research Center, Harbin Institute of Technology, Harbin 150080, China
  • Received:2017-12-12 Revised:2018-11-30 Online:2019-10-25 Published:2019-11-11
  • Contact: Ying WANG E-mail:wy@ncwu.edu.cn
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (11501199).

摘要: In this article we consider positive large solution of cooperative systems of the form -∆u1=λ1u1 + a1u1u2q1 -b1(x)u1p1+1, -∆u2=λ2u2 + a2u1q2u2 -b2(x)u2p2+1 in a bounded smooth domain Ω ⊂ RN(λiR, ai, bi>0, 0 < qi < pj, i, j ∈ {1, 2}, ij), Based on the construction of certain sup and sub-solution, we show existence, uniqueness and blow-up rate of the large solution.

关键词: cooperative system, blow-up rate, uniqueness

Abstract: In this article we consider positive large solution of cooperative systems of the form -∆u1=λ1u1 + a1u1u2q1 -b1(x)u1p1+1, -∆u2=λ2u2 + a2u1q2u2 -b2(x)u2p2+1 in a bounded smooth domain Ω ⊂ RN(λiR, ai, bi>0, 0 < qi < pj, i, j ∈ {1, 2}, ij), Based on the construction of certain sup and sub-solution, we show existence, uniqueness and blow-up rate of the large solution.

Key words: cooperative system, blow-up rate, uniqueness

中图分类号: 

  • 35J55