Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (5): 1363-1379.doi: 10.1007/s10473-019-0514-x

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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).

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

CLC Number: 

  • 35J55
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