数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (6): 2377-2387.doi: 10.1016/S0252-9602(12)60186-6

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SINGULAR POSITIVE RADIAL SOLUTIONS FOR A GENERAL SEMILINEAR ELLIPTIC EQUATION

杨芬   

  1. College of Science, Wuhan University of Science and Technology, Wuhan 430081, China
  • 收稿日期:2011-01-20 修回日期:2011-12-26 出版日期:2012-11-20 发布日期:2012-11-20
  • 基金资助:

    Supported by the Natural Science Foundation of China (10901126).

SINGULAR POSITIVE RADIAL SOLUTIONS FOR A GENERAL SEMILINEAR ELLIPTIC EQUATION

 YANG Fen   

  1. College of Science, Wuhan University of Science and Technology, Wuhan 430081, China
  • Received:2011-01-20 Revised:2011-12-26 Online:2012-11-20 Published:2012-11-20
  • Supported by:

    Supported by the Natural Science Foundation of China (10901126).

摘要:

The existence and uniqueness of singular solutions decaying like rm (see (1.4)) of the equation
Δu +∑kXi=ci|x|liupi = 0,        x ∈ Rn                              (0.1)
are obtained, where n ≥ 3, ci > 0, li > −2, i = 1, 2, · · · , k, pi > 1, i = 1, 2, · · · , k and the separation structure of singular solutions decaying like r−(n−2) of eq. (0.1) are discussed. moreover, we obtain the explicit critical exponent ps(l) (see (1.9)).

关键词: singular solution, decay, separation property, semilinear elliptic equation

Abstract:

The existence and uniqueness of singular solutions decaying like rm (see (1.4)) of the equation
Δu +∑kXi=ci|x|liupi = 0,        x ∈ Rn                              (0.1)
are obtained, where n ≥ 3, ci > 0, li > −2, i = 1, 2, · · · , k, pi > 1, i = 1, 2, · · · , k and the separation structure of singular solutions decaying like r−(n−2) of eq. (0.1) are discussed. moreover, we obtain the explicit critical exponent ps(l) (see (1.9)).

Key words: singular solution, decay, separation property, semilinear elliptic equation

中图分类号: 

  • 35J60